One of the major roadblocks to Financial Independence is to put your source of livelihood on one source of income. Anything with only one option creates high risk and is a major cause of stress when it’s uncertain. Thus, if your only source of income is full-time job, chances are high that you will postpone your financial independence. Worse of all is that this income lives and dies with your job.

Against this background, you are required to write an essay of 1500-2000 words on “**Online and Offline Opportunities for Money Making for Students, Graduates and Business people**”

Avoid copying and pasting because your work will be scanned for plagiarism,

The essay competition is ope for undergraduate and post graduate students in all Nigerian University.

Graduates who have left school in less than three years are also eligible to apply.

First Prize= N15,000

Second Prize=N10,000

Third Prize= N5,000

Submit your answers into the comment box.

Indicate your email address, phone no.and contact address

For students, kindly indicate your level, department and Institution

Deadline for Submission is 20th December, 2021.

Prizes shall be awarded in January, 2022.

You can send WhatsApp message to 080385592999 for more enquires

Level: 100 level

Department: Economics

Institution: University of Nigeria

Often times, people say that they can live without money. They define money as just one of the tools that enhances people’s living environment. However, in real life, money is a very important matter in people’s lives. Although, the people in history might have lived through the exchange of goods and not relying on the value of money itself, modern society today can not function without money. Money plays a huge role in the society in variety of ways such as in business, at people’s job and even in education. It helps people achieve a better quality of education, larger chance of business success and higher work output.

There are various means and opportunities for making money in today’s society. They include online and offline opportunities.

The online opportunities for making money involves the use of the internet. With the internet dominating over and influencing a large part of our lives, people look for ways to earn money online to increase their income streams. From freelance digital nomads to savvy marketers to rising entrepreneurs, there are plenty of ways to make money from the comfort of home using a laptop and a solid internet connection. Some online opportunities to obtain this, recently sourced out, include: Dropshipping, which is a business model where an individual sells a product to a customer but the supplier stores, packages and ships the product to the customers of the individual on his/her behalf.

Print on demand has also proven to be a popular option too. It is similar to dropshipping in the sense that you don’t need to carry inventory or ship out products to customers. Here, graphic designers turn to the business model to sell their designs on clothing and other products to monetize their art better. With their unique designs, they can create a consistent and established brand for their business.

Affiliate marketing is yet another way to make money online. It allows an individual to earn a living by promoting other brands. For instance, if you’re a savvy marketer, you can earn a commission from sales by promoting retail products, software, apps and more. While earning a commission may seem small, keep in mind that you can be an affiliate for several brands.

Another way is by starting a YouTube channel. Record shows that the highest paid YouTuber is 7 years old Ryan, who reviews toys on his YouTube channel, which made him $22 million in 2018. If an individual wants to begin a YouTube channel, he/she should remember to focus on a single niche so as to build a strong and loyal audience. The secret to making money on YouTube is to create content people want that either educated or entertains.

Creating online courses is another good opportunity to make money online. Sharing knowledge is one of the best ways to work towards that. If one is an expert on a subject, he/she can monetize his/her knowledge by creating courses online.

Other opportunities include: Becoming an influencer, Publishing an e-book, Blogging, Freelancing, Becoming a writer, Becoming an online tutor, Becoming a virtual assistant, Investing in stocks, Monetizing one’s photography, Selling clothes online, Trading cryptocurrencies, Reviewing websites, apps and software and so on. These online jobs make use of different websites which include Oberlo dropshipping, YouTube, Instagram, Amazon KDP, WordPress, Freelancer, Fiverr, Shopify, Tutor Me, Virtual assistant jobs, Indeed, Burst and many more.

By brainstorming online business ideas and choosing to start an online business, one can gain more financial freedom, improve their financial security and inch close to living life on their terms.

On the other hand, there are offline opportunities to make money. Unlike the online opportunities, the offline may require a little more legwork. They include: Selling gently used clothes which is a quick way to make some money. Starting with local consignment shops for faster cash or websites like Thredup and Poshmark to find buyers.

Trading in old phones and electronics is another option. An individual can sell his/her old phone, iPad or gaming system on sites like Swappa or Gazelle.

Getting a babysitting job is also not a bad opportunity. Everyone, from college students to recent retirees can make money by watching other people’s children. Word-of-mouth referrals from friends and family are still a great way to get started but one can also create a profile for free on sites like Care.com or Sittercity to expand their reach.

Renting out one’s car is yet another option to make money. Those who don’t use their cars for days or weeks at a time can rent out their car to individuals for cash.

Becoming a personal trainer is a great opportunity to make money offline as well. One can consider to become a personal trainer if he/she is in-the-know about fitness and nutrition. However, he/she may need some certification before beginning but could easily make some great money with just a few loyal personal trading clients.

Other opportunities include: Driving for Uber, Making deliveries for Amazon or Uber eats or Postmates, Finding work as a home sitter, Tutoring students, Finding a seasonal work and so on.

From all that has been mentioned so far, it is clear that there are many ways to make money whether online or offline. One can implement one or many of them. For instance, if you have experience in business or another field, you can always get paid to be a consultant. At the same time, you may also get engaged in publishing an e-book that is focused on a particular niche of audience thereby making your work different from other authors. All other combinations, just to get some cash, can be possible depending on how devoted the individual is

Nevertheless, it is not as easy as it seems to make money either way. Therefore, the individual needs to have a lot of patience, take his/her work seriously and be professional among other traits.

AN ESSAY WRITTEN FOR SUCCESS TONICS ESSAY COMPETITION

ONLINE AND OFFLINE OPPORTUNITIES FOR MONEY MAKING

FOR STUDENTS, GRADUATES, AND BUSINESS PEOPLE

December 2021

PROFILE

Name: Okoro, Izuchukwu Gospel

University: University of Nigeria, Nsukka

Department: English and Literary Studies

Level of Study: 200

Reg No: 2019/248092

Email address: izugokoro@gmail.com

Phone Number: 09035434039

Home Address: Amufia Village, Odenigwe, Nsukka, Enugu State.

ESSAY STYLE DETAILS

Font size: 12

Font Type: Times New Roman

Spacing: 1.5

Paper Size: A4

Page Count: 7

Word count: 1,843 (excluding preliminary pages)

Online and Offline Opportunities for Money Making for Students, Graduates, and Business People

Opportunity is missed by most people because it is dressed in overalls and looks like work.

–Â Thomas Edison, inventor and businessman.

In April of this year, I received a shocking news, one I haven’t recovered from in a long while. It was barely two weeks away from April Fool’s Day but this was not one, it was not even a joke. I had just heard what happened to my friend, Frank Egon, a student as at then in Enugu. From being an ordinary barman earning N25,000 naira monthly, Frank started earning N250,000 naira and even more, just by sitting at home, on his bed, and pressing his phone. Knowledge happened to him. Since it was neither a joke, nor him playing April Fool on me, I decided to seek knowledge like and from him, on money making opportunities in the offline and online world.

Well, have you ever been broke before? As a student, where you have to pay school fees, buy compulsory textbooks, pay departmental and faculty dues, and every other miscellaneous expenses that come up as a student, and you have little or no financial assistance from home, or you don’t have the money at all to do so, what do you do? Run to parents? Steal? I can tell you in all sincerity that I have found myself in this situation, coming from a humbled background where I have to train myself with little financial assistance whatsoever. This opened my eyes to countless opportunities that lie unused in the offline and online world.

You see, almost every time, people, especially students and youths, complain of being broke. What they fail to understand is that the difference between the zeros in their bank account and the millions other persons, even of their ages, make despite all of the talks on economic downturns is KNOWLEDGE. They simply lack knowledge, and like the proverbial Isrealites who perish from a lack of knowledge, they perish. However, one being equipped with the right knowledge of money making opportunities, both offline and online, is bound to begin his journey into realms of wealth, no matter how little he starts.

In the Offline World: Money Making Opportunities

If you don’t find a way to make money while you sleep, you will work until you die.

~ Warren Buffett

Every business is first set up offline, in some geographical location, in some shop or stall, neighborhood, or marketplace. If the owner is wise enough, it can be taken online to leverage the wider opportunities there for more cash flow.

The most interesting part of it is you may necessarily not need a huge capital to set up. So, no more excuses. A few offline opportunities that exist, and are proven are:

1. Tutoring: It’s not enough to be a brilliant nerd, have you thought of converting that brilliance you have into money? Tutoring is one offline business one can start without a capital. You just need to convince people, especially your coursemates, that in exchange for their money, you give them value for the courses (or subjects) they don’t understand during classes. Now, believe me you, no one wants to go home bearing the cross of FF’s. Like Jesus Christ, their parents would shout “crucify him”. Thus, it’s a good business one can start offline. One can also indulge in teaching Wassce, JAMB, and PUTME candidates where charges are either made per hour, periods, or heads. And if you’re good enough, you can be called in more than two places, giving you more chances to make more money. Flexibility and ease is the most beautiful aspect of this opportunity as it doesn’t get to interfere with your studies at school or your 9am-5pm job, or whatever occupies a major part of your life.

2. Storage Business: Jesus wittingly taught about this business using the parable of the five wise and foolish virgins. The wise virgins were smart enough to not only fill their lamps but to also carry extra should their lamps begin to die out. Now, that’s the same principle Joseph employed as Prime Minister of Egypt: storing enough foods such that the world came to buy from them. This is what storage business is about!

Knowing full well that certain important commodities would be needed when it’s not in season should be an enough reason to leverage on this opportunity. It gives you the monopoly in the marketplace because you and a select few, like the wise virgins, stored enough of them and are willing to sell them at an advantageous cost. You buy, re-bag, sell and have profits. Starting with as little as a bag of beans or melon seeds may not be much to you, but don’t they say that little drops of water make an ocean! Start small but go big.

3. Agriculture: this, suggestively, is the most profitable offline business venture to embark on. No matter how tough things are, people would still make sure to eat food. Even if they don’t eat well, they still must eat something little. Thus, going into farming– animal and crop– won’t be regrettable. This opportunity also accounts for over 75% of job opportunities in Nigeria and thus can stand as something you can start and with time employ others.

Now, as one progresses further, export can be taken into consideration. Export of cash crops and other indigenous crops that our overseas brethren desperately need. This gives one the opportunity to also earn in foreign currency.

4. Cyber Cafe Business: students have phones and systems loaded with data yet they don’t utilize it. First semester of last session at school saw me exploring this idea as I worked on students’ assignment and printed out for money in return. During exams like PUTME and CBT, your personal computer would be very useful in making some money by registering and typing and printing out documents for students.

5. Uber Driving: having a car is not enough, it is not for the luxury alone. As much as it was primarily bought for that sake, on weekends, it could be used to convey people from place to place as a special chartered taxi. Companies like Bolt offers this opportunity. Big men who make use of this service pay a lot for it and this provides you a means of income and luxury on the other hand.

6. Ushering Agency: believe me you, this idea has been left in the gallows for a while. Whether you’re a student or a graduate, you can start up an agency that will help manage events and usher men into comfortable seats. Tall, elegant, intelligent ladies (and guys) are needed here. This gives one an opportunity to convert beauty and class to money.

7. Salon: like the Jewish Phenomenon where one is expected to have a skill at a young age, Nigerians should have a skill. Such skill can involve making and cutting hair. Because people won’t always look untidy, no matter how much poverty exists, you can convert your hair-making and barbing skills to money. You may start without a shop, but never lack going to hostels, homes, churches, public places to advertise your skills.

Though, the opportunities here are still limitless, however it can be tedious having to work from place to place when from the comfort of your house, you can still earn money.

Online World of Money Making Opportunities

Money is multiplied in practical value depending on the number of W’s you control in your life: what you do, when you do it, where you do it, and with whom you do it.

–Â Timothy Ferriss, author of The 4-Hour Workweek.

One of the best things about the internet is that you can get into a business by yourself, and meet a network of clients from all over the world, flexible and remote to work. To say that it helps you work according to your schedules even as a student or employee, is even more interesting.

1. Freelancing: whatever skills you have, you can be contracted for a part-time job. From photography, to writing, to teaching, to typing or transcribing, to whatever you can do, you can work as a freelancer, earning in foreign currency. Check up sites like Upwork, Fiverr, Freelancer dot com, etc, to set up an account and start bidding for jobs. Pretty easy!

2. Blogging: you can write, there is a whole lot of money opportunities coming your way. The internet is replete with examples of men and women who bought expensive cars and built

mansions through blogging. Wondering how? Blogging works based on traffic generated, and one way to do that is through Google AdSense. There, you get to advertise people’s products and ideas for Google and get paid for it. It’s a great idea because you can do it during your spare time if you don’t want to be a full time blogger.

3. Affiliate Marketing: a scheme where people sell the products of other persons and get paid for it is affiliate marketing. As simple as it is, you are not buying any product but you get paid for as many customers that buy through your unique link. Few youths who are able to pay the price and pick up an affiliate marketing skill, with diligence, have proven to be rich in no little time.

4. Online Jobs: there are a lot of jobs to do online that suits your taste and passion. If you love playing games, reading books, listening to music, typing, social media-ing, writing, singing, there’s an application software specially built for that. There are also sites that grant a million others and you that job. The only reason you’re surprised is that you have no slight knowledge about this. Now, go and surf the net!

5. Crypto Currency Exchange: with the society going cashless, the use and sale of coins is now a norm, and a means of making money. There are certain coins that have the potential of rising, to make more cash inflow; get them! trade and make profit.

6. Forex Trading: might be quite tasking but with proper trainings and mentorship, one is bound to make lots of money. This is a kind of trade that involves buying a currency while selling another and as such the risks here are potentially high. But is living life itself not the greatest risk? Thus, with a dedicated strategy and determination of heart, one is bound to roll in some bucks into his account.

Conclusion

God was wise when He created the sun to shine at day and the moon at night; meaning when one stream of income stops, there should be another to replace it. Moving a step further, God showed us this financial independence strategy using the seven rivers that flow in to water Eden; meaning have more than one stream of income. Diversifying your streams of income through offline and online money making opportunities is one step to gaining financial independence.

NAME: ATTAMA LILLIAN OGECHUKWU

REG NO: 2019/243411

Write short notes on:

Poisson Distribution

In statistics, a Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period. In other words, it is a count distribution. Poisson distributions are often used to understand independent events that occur at a constant rate within a given interval of time. It was named after French mathematician SimÃ©on Denis Poisson.

The Poisson distribution is a discrete function, meaning that the variable can only take specific values in a (potentially infinite) list. Put differently, the variable cannot take all values in any continuous range. For the Poisson distribution (a discrete distribution), the variable can only take the values 0, 1, 2, 3, etc., with no fractions or decimals.

Poisson distribution can be used to estimate how likely it is that something will happen “X” number of times. For example, if the average number of people who buy cheeseburgers from a fast-food chain on a Friday night at a single restaurant location is 200, a Poisson distribution can answer questions such as, “What is the probability that more than 300 people will buy burgers?” The application of the Poisson distribution thereby enables managers to introduce optimal scheduling systems that would not work with, say, a normal distribution.

Uniform Distribution

A uniform probability distributions one in which all elementary events in the sample space have an equal opportunity of occurring that is each event occurring has an equal chance. As a result, for a finite sample space of size n, the probability of an elementary event occurring is 1/n.

Exponential Distribution

This is usually present when we are dealing with events that are rapidly changing early on for eg news and blog. The exponential distributions wildly used in the field of reliability. Reliability deals with the amount of time a product lasts. Its probability function is represented as; P(X=x) = me-mx.

Six (6) doctors and twenty (20) nurses attend a small conference. All 26 names are put in a hat, and 7 names are selected without replacement. What is the probability that 4 doctors and 3 nurses are picked?

Solution

P(X=x)= r N-r

x n-x

N

n

= N = 6+20 = 26

r = 6

n = 7

x = 4

P(X=4) = 6 26-6

4 7-4

26

7

P(X=4) = 6C4 X 20C3

26C7

P(X=4) = 15X1140/657800

P(X=4) = 17100/657800

= 0.0025995743

= 0.0260. 4dp

Using the geometric approach, suppose that the probability of female celebrity getting married is 0.35, find the probability that she wll actually get married in her 8th relationship.

Solution

P(X=x)=Pqx

P= 0.35

q= 1-p, 1-0.35= 0.65

x= 8-1= 7 (number of failures)

P(X=7) = 0.35x(0.65)7

= 0.017157

= 0.017157×100

= 1.7% chance.

To make a dozen chocolate cookies, 50 chocolate chips are mixed into a dough. The same proportion is used for all batches. If a cookie is chosen at random from a large batch, also using landa (the mean) to the nearest whole number. What is the probability that it contains;

No chocolate chips

Solution

P(X=x) = e-Æ›Æ›x/x!

Æ› = 50/12 = 4 (to the nearest whole number)

P(X=0) = e-4(4)0/0! = 0.0183

7 chocolate chips

Solution

P(X=x) = e-Æ›Æ›x/x!

Æ› = 50/12 = 4 (to the nearest whole number)

P(X=7) = e-4(4)7/7! = 0.0595

Name: Onyeleonu precious Oluomachi

Reg no: 2019/248162

Write short notes on:

POISSON PROBABILITY DISTRIBUTION:

This is a discrete probability distribution derived by a French Mathematician/Physicist, SIMEON POISSON in 1837..

It arises frequently in counting number of random events in a given interval of time of space in a particular area of opportunity..

WHEN TO APPLY POISSON DISTRIBUTION

a) When we want to determine the number of times and event occured in a given area of opportunity..

b)When the number of times and event occured in one area is independent of the number of times and event occured in another area of opportunity.

c)When the probability of events occuring in an area becomes zero as the area of occurance becomes smaller..

POISSON PROBABILITY FUNCTION: e-^ ^X/x!

-Where x=random variables

-The symbol e(exponential)(the base of the natural logritgm system)is a constant =2.71282

-The Greek letter Lamb is called the parameter of the distribution, represents average number of times the random variable occurs in a specified interval of time or space..

UNIFORM PROBABILITY DISTRIBUTION

This is a type of continuous distribution which is used in rounding errors when measurements are recorded to some degree of accuracy. The parameters a and B which form the two boundaries of the interval over which the distribution is defined are the two parameters that completely specified the distribution..

The density function forms a rectangle with base B-a and constant height (B-a),as a result,the uniform distribution is often called RECTANGULAR DISTRIBUTION.The application of this distribution is often based on assumption that the probability of falling in an interval of fixed length with (a-B) is constant.

This distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. It is often abbreviated as U(a-B), where U stands for uniform distribution..

The difference between the bounds defines the interval lenght. All intervals of the same length on the distribution’s support,are equally probable..

Exponential Distribution

This is usually present when we are dealing with events that are rapidly changing early on for eg news and blog. The exponential distributions wildly used in the field of reliability. Reliability deals with the amount of time a product lasts. Its probability function is represented as; P(X=x) = me-mx.

2. Six (6) doctors and twenty (20) nurses attend a small conference. All 26 names are put in a hat, and 7 names are selected without replacement. What is the probability that 4 doctors and 3 nurses are picked?

Solution

P(X=x)= r N-r

x n-x

N

n

= N = 6+20 = 26

r = 6

n = 7

x = 4

P(X=4) = 6 26-6

4 7-4

26

7

P(X=4) = 6C4 X 20C3

26C7

P(X=4) = 15X1140/657800

P(X=4) = 17100/657800

= 0.0025995743

= 0.0260. 4dp

3. Using the geometric approach, suppose that the probability of female celebrity getting married is 0.35, find the probability that she wll actually get married in her 8th relationship.

Solution

P(X=x)=Pqx

P= 0.35

q= 1-p, 1-0.35= 0.65

x= 8-1= 7 (number of failures)

P(X=7) = 0.35x(0.65)7

= 0.017157

= 0.017157×100

= 1.7% chance.

4. To make a dozen chocolate cookies, 50 chocolate chips are mixed into a dough. The same proportion is used for all batches. If a cookie is chosen at random from a large batch, also using landa (the mean) to the nearest whole number. What is the probability that it contains;

No chocolate chips

Solution

P(X=x) = e-Æ›Æ›x/x!

Æ› = 50/12 = 4 (to the nearest whole number)

P(X=0) = e-4(4)0/0! = 0.0183

7 chocolate chips

Solution

P(X=x) = e-Æ›Æ›x/x!

Æ› = 50/12 = 4 (to the nearest whole number)

P(X=7) = e-4(4)7/7! = 0.0595

Daniel Unique Agbenu

2019/246710

Economics department

uniquedaniel08@gmail.com

1.Write short notes on the following types of probability distributions

a. Poission probability distribution

Poisson distribution is used when you are interested in the number of times an event occurs in a given area of opportunity. An area of opportunity is a continuous unit or interval of time, volume or such area more than one occurrence of an event can occur. is used to show how many times an event is likely to occur over a specified period. The Poisson distribution is a discrete function, meaning that the variable can only take specific values in a (potentially infinite) list. In other words, it is a count distribution. Poisson distributions are often used to understand independent events that occur at a constant rate within a given interval of time. Poisson distribution can be used to estimate how likely it is that something will happen “X” number of times.

Poisson distribution Formula

P(X=x) = e-Î». Î»x/x!

Where e is Euler’s number (e = 2.71828…)

x is the number of occurrences or number of events in an area of opportunity.

x! is the factorial of x

Î» is equal to the expected value or expected number of events(EV) of x when that is also equal to its variance

b. Uniform Probability Distribution

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. Under a uniform distribution, each value in the set of possible values has the same possibility of happening.A coin also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.Uniform distribution is a probability distribution that asserts that the outcomes for a discrete set of data have the same probability.

In a discrete uniform distribution, outcomes are discrete and have the same probability.In a continuous uniform distribution, outcomes are continuous and infinite.In a normal distribution, data around the mean occur more frequently.

The notation for the uniform distribution is X ~ U(a, b) where a = the lowest value of x and b = the highest value of x.

The probability density function is f(x)=

1/bâˆ’a for a â‰¤ x â‰¤ b.

c. Exponential Probability Distribution.

The exponential distributidon is often concerned with the amount of time until some specific event occurs.Exponential distributions are commonly used in calculations of product reliability, or the length of time a product lasts.Values for an exponential random variable occur in the following way. There are fewer large values and more small values. For example, the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are more people who spend small amounts of money and fewer people who spend large amounts of money.

2. Using the hypergeometric method to solve the equation

Formula isP(X=x) = [rCx] [N-rn-x] Ã·[NCn]

Where x= number of successes in the number of trials n

N= total number of elements in the population

r= number of successes in the population

N-r = numbe of failures in the population

n= number of trials(sample size)

N= 6+20=26 r=6 n=7 x=4 N-r =20. n-x=3

6C4*20C3Ã·26C7. = 15*1,140Ã·675,800

= 17,100Ã·675,800

=0.025303

3. Using the geometric distribution method

P(X=x) = P(1-P) raise to power x or pqraise to power x

P =0.35. ( 1-P) =1-0.35=0.65

x will be the number of her relationships before marriage

P(X=7) = (0.35*(0.65)*7

= 0.35*0.049022 = 0.01757

4. Using the Poisson distribution method

P(X=x) = e-Î». Î»x/x!

Where e is Euler’s number (e = 2.71828…)x is the number of occurrences or number of events in an area of opportunity.

x! is the factorial of x

Î» is equal to the expected value or expected number of events(EV) of x when that is also equal to its variance

Î» to the nearest whole number = 50Ã·12= 4.166= 4

For no cholocate: x=0

e raise to the power of -4*4raise to power 0Ã·0!

= 0.0183*1Ã·1= 0.0183

For 7 chocolate chips;x=7

Î»= 4 = 0.0183 *4raise to power 7Ã· 7!

=0.0183*16,384Ã·5,040

=299.8272Ã·5040

= 0.05948

1.Write short notes on the following types of probability distributions:

Poisson probability distribution: it is used to show how many times an event is likely to occur over a specified period. It is a discrete function by which variable can take only a specified value in a list Examples include number of mosquito bite on person, number of computer crashes in a day etc.

Uniform probability distribution: it is also known as Continuous uniform distribution or rectangular distribution. It is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.

Exponential probability distribution: it is a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the probability distribution of the time between events in a Poisson point process.

2.Six [6] doctors and twenty [20] nurses attended a small conference all 26 names are put in a hat, 7 names are randomly selected without replacement. What is the probability that 4 doctors and 3 nurses are picked?

P {X=4 doctors and 3 nurses}

N=6+20=26

n=7

r=6

x= 4 doctors 3 nurses

P{X=x} =[rCx][N-rCn-x]/NCn

=(6C4) (20C3)/26C7

= 15Ã—1140/657800

= 17100/657800

= 0.0260.

Using the geometric approach, suppose that the probability of female celebrity getting married is 0.35. find the probability that she will get married in her 8th relationship?

3. P(X=x) Pqx

P= 0.35

q= 1-p = 1-0.35= 0.65

x = x-1 = 8-1= 7.

P(x=7) = 0.35 Ã—

= 0.0172

4.To make a dozen chocolate chips cookies, 50 chocolate chips are mixed into the dough. The same proportion is used for all batches. If a chocolate is chosen at random from a batch, also using lamda too the nearest whole number. What is the probability that it contains?

No chocolate

7 chocolates.

P(x=0)

4Â°Ã—2.7183^-4/1!

1Ã—0.0183/1!

=0.0183

P(x=7)

4^7 Ã— 2.7193^-4/7!

=16384Ã—0.0183/5040

=299.8272/5040

=0.0595.

Ugwuanyi Nkeonye Laurel

2019/243315

nkemlaurel@gmail.com

1. Poisson distribution

In statistics, a Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.

A Poisson distribution can be used to estimate how likely it is that something will happen “X” number of times. For example, if the average number of people who buy cheeseburgers from a fast-food chain on a Friday night at a single restaurant location is 200, a Poisson distribution can answer questions such as, “What is the probability that more than 300 people will buy burgers?”

e is Euler’s number (e = 2.71828…)

x is the number of occurrences

x! is the factorial of x

Î» is equal to the expected value (EV) of x when that is also equal to its variance

It can be used to estimate how many times an event is likely to occur within “X” periods of time.

Poisson distributions are used when the variable of interest is a discrete count variable.

Many economic and financial data appear as count variables, such as how many times a person becomes unemployed in a given year, thus lending themselves to analysis with a Poisson distribution.

Uniform distribution

A uniform distribution, also called a rectangular distribution, is a probability distribution that has constant probability.

This distribution is defined by two parameters, a and b:

a is the minimum.

b is the maximum.

The distribution is written as U(a, b).

The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.

The probability density function is

F(x)= 1/b-a

for a â‰¤ x â‰¤ b.

Uniform distributions are probability distributions with equally likely outcomes.

In a discrete uniform distribution, outcomes are discrete and have the same probability.

In a continuous uniform distribution, outcomes are continuous and infinite.

In a normal distribution, data around the mean occur more frequently.

The frequency of occurrence decreases the farther you are from the mean in a normal distribution.

Exponential distribution

The exponential distribution is one of the widely used continuous distributions. It is often used to model the time elapsed between events. We will now mathematically define the exponential distribution, and derive its mean and expected value. Then we will develop the intuition for the distribution and discuss several interesting properties that it has.

A continuous random variable X is said to have an exponential distribution with parameter Î»>0, shown as Xâˆ¼Exponential(Î»),

The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the length, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. It can be shown, too, that the value of the change that you have in your pocket or purse approximately follows an exponential distribution.

2. P(x-r) =. (rCx * N-rCn-x)/ NCn

N= 6+20 =26

r=6

n=7

X =4

P(X=4)= (6C4 Ã— 26-6C7-4)\ 26C7

P(X=4) = (6C4 Ã— 20C3)/26C7

P(X=4)= 0.0024995743

~0.0025

3. P(X=X) = owe

P= 0.35

q= 1-0.35 = 0.65

P(X=7)= 0.35Ã—0.65^7

0.35Ã—0.0490

= 0.0172

4. P(x; Î¼) = (e^-Î¼) (Î¼^x) / x!

e= 2.7183

Î¼= 50/12 = 4.167

I. P(X=0) =

(2.7183^-4.167)(4.167^0)/0!

P(X=0) = 0.015498

~0.0155

ii. P(X=7) =

(2.7183^-4.167)(4.167^7)/7!

(0.015498Ã—21815.4664)/5040

=0.06708

~0.067

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