Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Textbook Question
Chapter 7, Problem 33RE
Quality control A product must pass an initial inspection, where the probability that it will be rejected is 0.2. If it passes this inspection, it also must pass a second inspection where the probability that it will be rejected is 0.1. What is the probability that it will pass both inspections?
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6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows:
P(X=-x) = P(X = x)=p. P(X=0)= 1-2p.
Show that there is equality in Chebyshev's inequality for X.
This means that Chebyshev's inequality, in spite of being rather crude, cannot be
improved without additional assumptions.
4. Prove that, for any random variable X, the minimum of EIX-al is attained for
a = med (X).
8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined
as a product of independent, identically distributed random variables with mean
1 (under the so-called null hypothesis), and the, sometimes more convenient,
log-likelihood, log L, which was a sum of independent, identically distributed
random variables, which, however, do not have mean log 1 = 0.
(a) Verify that the last claim is correct, by proving the more general statement,
namely that, if Y is a non-negative random variable with finite mean, then
E(log Y) log(EY).
(b) Prove that, in fact, there is strict inequality:
E(log Y) < log(EY),
unless Y is degenerate.
(c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a
glimpse on (b).
Chapter 7 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 7.1 - CHECKPOINT
1. If a coin is drawn from a box...Ch. 7.1 - CHECKPOINT
2. A ball will be drawn from a bag...Ch. 7.1 - CHECKPOINT
3. A coin is tossed, and a die is...Ch. 7.1 - 1. One ball is drawn at random from a bag...Ch. 7.1 - 2. One ball is drawn at random from a bag...Ch. 7.1 - 3. If you draw one card at random from a deck of...Ch. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - 6. A die is rolled. What is the probability...Ch. 7.1 - 7. An urn contains three red balls numbered 1, 2,...
Ch. 7.1 - 8. An urn contains three red balls numbered 1, 2,...Ch. 7.1 - 9. From a deck of 52 ordinary playing cards, one...Ch. 7.1 - 10. From a deck of 52 ordinary playing cards, one...Ch. 7.1 - 11. Suppose a fair coin is tossed two times....Ch. 7.1 - Prob. 12ECh. 7.1 - 13. Use Table 7.1 to determine the following...Ch. 7.1 - 14. (a) When a pair of distinguishable dice is...Ch. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - 17. Suppose a die is tossed 1200 times and a 6...Ch. 7.1 - 18. Suppose that a coin is tossed 3000 times and...Ch. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - 21. If the odds that a particular horse will win a...Ch. 7.1 - 22. If the odds that an event E will not occur are...Ch. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - 25. Car maintenance A car rental firm has 425...Ch. 7.1 - Prob. 26ECh. 7.1 - 27. Voting The table gives the average number of...Ch. 7.1 - Prob. 28ECh. 7.1 - 29. Sales promotion In a sales promotion, a...Ch. 7.1 - 30. Management A dry cleaning firm has 12...Ch. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - 33. Blood types Human blood is classified by blood...Ch. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - 39. Fraud A company selling substandard drugs to...Ch. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - 44. Quality control A supply of 500 plasma...Ch. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - 48. Quality control A computer store offers used...Ch. 7.1 - 49. Genetics A newly married couple plan to have...Ch. 7.1 - 50. Management A frustrated store manager is asked...Ch. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - 64. Ice cream The odds of an American home having...Ch. 7.1 - Prob. 65ECh. 7.1 - 66. Rain If the probability of rain today is ,...Ch. 7.1 - Prob. 68ECh. 7.2 - CHECKPOINT
1. If a ball is drawn from a bag...Ch. 7.2 - Prob. 2CPCh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - In Problems 1-4, one card is drawn from a deck of...Ch. 7.2 - Prob. 4ECh. 7.2 - 5. An ordinary die is tossed. What is the...Ch. 7.2 - 6. A card is drawn at random from a deck of 52...Ch. 7.2 - 7. If the probability that event E will occur is...Ch. 7.2 - Prob. 8ECh. 7.2 - In Problems 9-12, one ball is drawn from a bag...Ch. 7.2 - In Problems 9-12, one ball is drawn from a bag...Ch. 7.2 - Prob. 11ECh. 7.2 - In Problems 9-12, one ball is drawn from a bag...Ch. 7.2 - 13. Suppose a die is biased (unfair) so that each...Ch. 7.2 - Prob. 14ECh. 7.2 - 15. A bag contains 4 white, 7 black, and 6 green...Ch. 7.2 - 16. In a game where only one player can win, the...Ch. 7.2 - 17. A cube has 2 faces painted red, 2 painted...Ch. 7.2 - Prob. 18ECh. 7.2 - 19. A ball is drawn from a bag containing 13 red...Ch. 7.2 - 20. A ball is drawn from a bag containing 13 red...Ch. 7.2 - 21. Drug use Forty-six percent of marijuana use...Ch. 7.2 - 22. Breast cancer According to the American Cancer...Ch. 7.2 - 23. Car maintenance A car rental firm has 425...Ch. 7.2 - 25. Linguistics Of 100 students, 24 can speak...Ch. 7.2 - 25. Linguistics Of 100 students, 24 can speak...Ch. 7.2 - 26. Management A company employs 65 people. Eight...Ch. 7.2 - Prob. 27ECh. 7.2 - 28. Mountain biking Rob Lee knows that he can...Ch. 7.2 - 29. Salaries The table gives the percent of...Ch. 7.2 - Prob. 30ECh. 7.2 - 31. Workers The table gives the projected number...Ch. 7.2 - 32. Causes of death In the United States in 2014,...Ch. 7.2 - 33. HIV cases The table gives the numbers of new...Ch. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - 37. Education A mathematics class consists of
16...Ch. 7.2 - 38. Parts delivery Repairing a copy machine...Ch. 7.2 - Oil drilling The table summarizes the opinions of...Ch. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - 43. Drinking age A survey questioned 1000 people...Ch. 7.2 - 44. Job bids Three construction companies have bid...Ch. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.3 - CHECKPOINT
1. Suppose that one ball is drawn from...Ch. 7.3 - Prob. 2CPCh. 7.3 - CHECKPOINT
3. Two balls are drawn with replacement...Ch. 7.3 - 1. A card is drawn from a deck of 52 playing...Ch. 7.3 - Prob. 2ECh. 7.3 - 3. A die has been “loaded so that the probability...Ch. 7.3 - 4. A die has been “loaded” so that the probability...Ch. 7.3 - 5. A bag contains 9 red balls numbered 1, 2, 3, 4,...Ch. 7.3 - Prob. 6ECh. 7.3 - 7. A bag contains 4 red balls and 6 white balls....Ch. 7.3 - 8. A fair die is rolled. Find the probability that...Ch. 7.3 - 9. A fair coin is tossed 3 times. Find the...Ch. 7.3 - 10. A fair coin is tossed 14 times. What is the...Ch. 7.3 - 11. A die is thrown twice. What is the probability...Ch. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - 15. (a) A box contains 3 red balls, 2 white balls,...Ch. 7.3 - Prob. 16ECh. 7.3 - 17. Two balls are drawn from a bag containing 3...Ch. 7.3 - Prob. 18ECh. 7.3 - 19. A bag contains 9 nickels, 4 dimes, and 5...Ch. 7.3 - Prob. 20ECh. 7.3 - 21. A red ball and 4 white balls are in a box. If...Ch. 7.3 - 22. From a deck of 52 playing cards, two cards are...Ch. 7.3 - 23. One card is drawn at random from a deck of 52...Ch. 7.3 - Prob. 24ECh. 7.3 - 25. Two balls are drawn without replacement from a...Ch. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Carbon emissions The table gives the results of a...Ch. 7.3 - Prob. 30ECh. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Oil drilling Suppose the table summarizes the...Ch. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - 43. Quality control Each computer component that...Ch. 7.3 - Prob. 44ECh. 7.3 - 45. Lactose intolerance Lactose intolerance...Ch. 7.3 - 46. Quality control If 3% of all light bulbs a...Ch. 7.3 - 47. Quality control To test its shotgun shells, a...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - 53. Maintenance Twenty-three percent of the cars...Ch. 7.3 - Prob. 54ECh. 7.3 - 55. Testing An unprepared student must take a...Ch. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - 58. Racing Suppose that the odds that Blackjack...Ch. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - 62. Crime In an actual case.’ probability was used...Ch. 7.4 - CHECKPOINT
1. Urn I contains 3 gold coins, urn II...Ch. 7.4 - Prob. 2CPCh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 2ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 4ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 6ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - In Problems 1-12, use probability trees to find...Ch. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - Prob. 14ECh. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - In Problems 13-16, use (a) a probability tree and...Ch. 7.4 - 17. Lactose intolerance Lactose intolerance...Ch. 7.4 - 18. Genetics What is the probability that a couple...Ch. 7.4 - 19. Marksmanship Suppose that a marksman hits the...Ch. 7.4 - 20. Majors In a random survey of students...Ch. 7.4 - 21. Quality control Suppose a box contains 3...Ch. 7.4 - 22. Education The probability that an individual...Ch. 7.4 - 23. Alcoholism A small town has 8000 adult males...Ch. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - 26. Insurance rates Ideally, auto insurance rates...Ch. 7.4 - 27. Pregnancy test A self-administered pregnancy...Ch. 7.4 - Prob. 28ECh. 7.4 - 29. Survey In a Student Activity Participation...Ch. 7.4 - Prob. 30ECh. 7.5 - CHECKPOINT
1. If a state permits either a letter...Ch. 7.5 - Prob. 2CPCh. 7.5 - Prob. 3CPCh. 7.5 - Prob. 4CPCh. 7.5 - Prob. 5CPCh. 7.5 - 1. Compute .
Ch. 7.5 - Prob. 2ECh. 7.5 - 3. Compute .
Ch. 7.5 - 4. Compute .
Ch. 7.5 - 5. Compute .
Ch. 7.5 - Prob. 6ECh. 7.5 - 7. How many four-digit numbers can be formed from...Ch. 7.5 - Prob. 8ECh. 7.5 - 9. Compute .
Ch. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - 15. Compute .
Ch. 7.5 - 16. Compute .
Ch. 7.5 - 17. Compute .
Ch. 7.5 - Prob. 18ECh. 7.5 - 19. Compute .
Ch. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - 23. Binz, not Benz Mercedes Benz E-Class sedans...Ch. 7.5 - 24. Ice cream cones Baskin-Robbins’logo includes...Ch. 7.5 - Prob. 25ECh. 7.5 - 26. Menu selections A restaurant has an early...Ch. 7.5 - Prob. 27ECh. 7.5 - 28. Racing Eight horses are entered in a race. In...Ch. 7.5 - Prob. 29ECh. 7.5 - 30. Testing An examination consists of 12...Ch. 7.5 - Prob. 31ECh. 7.5 - Prob. 32ECh. 7.5 - 33. Management A department store manager wants to...Ch. 7.5 - 34. Call letters The call letters for radio...Ch. 7.5 - Prob. 35ECh. 7.5 - 36. Testing How many ways can a 10-question...Ch. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - 40. Astronauts If 8 people are qualified for the...Ch. 7.5 - 41. Sales A traveling salesperson has 30 products...Ch. 7.5 - Prob. 42ECh. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - 47. Committees In how many ways can a committee...Ch. 7.5 - Prob. 48ECh. 7.5 - Prob. 49ECh. 7.5 - 50. Auto dealerships An auto dealer has 4 cars, 2...Ch. 7.6 - CHECKPOINT
1. If three wires (red, black, and...Ch. 7.6 - Prob. 2CPCh. 7.6 - 1. Education If a child is given cards with A, C,...Ch. 7.6 - Prob. 2ECh. 7.6 - Politics A poll asks voters to rank Social...Ch. 7.6 - 4. Photography Two men and a woman are lined up to...Ch. 7.6 - 5. License plates Suppose that all license plates...Ch. 7.6 - Prob. 6ECh. 7.6 - 7. ATMs
(a) An automatic teller machine requires...Ch. 7.6 - 8. Keys Keys for antique General Motors cars had...Ch. 7.6 - 9. Phone numbers If the first digit of a...Ch. 7.6 - Prob. 10ECh. 7.6 - 11. Rewards As a reward for a record year, the Ace...Ch. 7.6 - 12. Mutual funds The retirement plan for a company...Ch. 7.6 - 13. Testing In a 10-question matching test with 10...Ch. 7.6 - Prob. 14ECh. 7.6 - 15. Quality control A box of 12 batteries has 3...Ch. 7.6 - 16. Quality control Suppose that 6 batteries are...Ch. 7.6 - 17. Quality control A retailer purchases 100 of a...Ch. 7.6 - Prob. 18ECh. 7.6 - 19. Banking To see whether a bank has enough...Ch. 7.6 - 20. Diversity A high school principal must select...Ch. 7.6 - 21. Diversity Suppose that an employer plans to...Ch. 7.6 - 22. Lottery Four men and three women are...Ch. 7.6 - Prob. 23ECh. 7.6 - 24. Sales A car dealer has 12 different cars that...Ch. 7.6 - 25. Diversity Suppose that two openings on an...Ch. 7.6 - Prob. 26ECh. 7.6 - 27. Management Suppose that an indecisive company...Ch. 7.6 - 28. Quality control Suppose that 10 computer chips...Ch. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - 32. Evaluation Employees of a firm receive annual...Ch. 7.6 - Prob. 33ECh. 7.6 - Prob. 34ECh. 7.6 - 35. Poker A flush (5 cards from the same suit) is...Ch. 7.6 - Prob. 36ECh. 7.6 - Prob. 37ECh. 7.7 - Prob. 1CPCh. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Prob. 2ECh. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Can the vectors in Problems 1-4 be probability...Ch. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - In Problems 9-12, use the given transition matrix...Ch. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Prob. 14ECh. 7.7 - 15. Use the matrix and initial probability vector...Ch. 7.7 - Prob. 16ECh. 7.7 - In Problems 17-20, find the steady-state vector...Ch. 7.7 - Prob. 18ECh. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Politics Use the following information for...Ch. 7.7 - Prob. 22ECh. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Church attendance Use the following information...Ch. 7.7 - Prob. 26ECh. 7.7 - Car selection Use the following information for...Ch. 7.7 - Prob. 28ECh. 7.7 - Prob. 29ECh. 7.7 - Prob. 30ECh. 7.7 - Prob. 31ECh. 7.7 - Car selection Use the following information for...Ch. 7.7 - 33. Population demographics Suppose a government...Ch. 7.7 - Prob. 34ECh. 7.7 - Prob. 35ECh. 7.7 - Prob. 36ECh. 7.7 - Prob. 37ECh. 7.7 - Prob. 38ECh. 7.7 - Prob. 39ECh. 7.7 - Prob. 40ECh. 7 - 1. If one ball is drawn from a bag containing 9...Ch. 7 - 2. Suppose a ball is drawn from a bag containing 9...Ch. 7 - 3. If the probability that an event E occurs is...Ch. 7 - 4. Suppose that a fair coin is tossed two times....Ch. 7 - 5. Suppose that a fair coin is tossed three times....Ch. 7 - 6. A card is drawn at random from an ordinary deck...Ch. 7 - 7. A deck of 52 cards is shuffled. A card is...Ch. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - 11. A bag contains 4 red balls numbered 1, 2, 3, 4...Ch. 7 - 12. A bag contains 4 red balls and 3 black balls....Ch. 7 - 13. A box contains 2 red balls and 3 black balls....Ch. 7 - Prob. 14RECh. 7 - 15. A bag contains 8 white balls, 5 red balls, and...Ch. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - 19. Bag A contains 3 red, 6 black, and 5 white...Ch. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - 23. How many combinations of 8 things taken 5 at a...Ch. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - 26. Find the steady-state vector associated with...Ch. 7 - 27. Senior citizens In a certain city, 30,000...Ch. 7 - Prob. 28RECh. 7 - 29. United Nations Of 100 job applicants to the...Ch. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Productivity Suppose that in a study of leadership...Ch. 7 - 33. Quality control A product must pass an initial...Ch. 7 - 34. Auto styles A certain make of car comes with...Ch. 7 - Prob. 35RECh. 7 - 36. Purchasing A regional survey found that of...Ch. 7 - 37. Quality control In a manufacturing process...Ch. 7 - 38. Management A personnel director ranks 4...Ch. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - 42. Juries A jury will be deadlocked if one or...Ch. 7 - 43. License plates The RBC Heritage Classic...Ch. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - 47. Lottery If a person “boxes” (see Problem 46) a...Ch. 7 - 48. Quality control A supplier has 200 compact...Ch. 7 - 49. Stocks Mr. Way must sell stocks from 3 of the...Ch. 7 - 50. Quality control A sample of 6 fuses is drawn...Ch. 7 - Income levels Use the following information for...Ch. 7 - Prob. 52RECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - A bag contains three white balls numbered 1, 2, 3...Ch. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - 10. A cat hits the letters on a computer keyboard...Ch. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - 16. Computer chips come from two suppliers, with ...Ch. 7 - 17. A placement test is given by a university to...Ch. 7 - 18. Lactose intolerance affects about of...Ch. 7 - Prob. 19TCh. 7 - Prob. 20TCh. 7 - Prob. 21TCh. 7 - 22. A publishing company has determined that a new...
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Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License