Chapter 6

Discrete Probability Distributions

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Assignment

(32 points due by 11 pm February 10th)

Note: You can team up with one of your classmates to complete the assignment (not more than two in a team); if you want to work on the assignment individually, that’s also fine. If you are working in teams, then only one submission is required per team; include both the team members’ last names as part of the assignment submission file name as well as in the assignment submission document.

Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 8 points each):

1) A die is tossed.

a) List all possible outcomes.

b) Let X equal 0 if the die shows a value or 1 or 2; let X equal 1 if the die shows a value of 3; and let X equal 2 if the die shows a value greater than 3. What is the P (X=0)? P (X=1)? P (X=2)?

2) A random variable has possible values of 20, 21, 22, 23, and 24 that are equally likely to occur.

a) What is the probability that the random variable is less than 23?

b) What is the mean of the random variable?

c) What is the standard deviation of the random variable?

3) Mergers and slow periods in the economy often result in layoffs at many firms. Many employees count on two or three months of severance pay to carry them over to the next job. However, job searches can sometimes take longer than 6 months. A survey of workers who have been with firms for more than a year revealed that only 30% of the workers would be financially secure if they lost their jobs for 6 months to a year. Let X represent the number of employees out of a sample of 80 who would feel financially secure if they lost their job for 6 months to a year.

a) What is the probability that at least 30 employees out of 80 would be financially secure if they lost their job for 6 months to a year?

b) Do a ‘what-if’ analysis by changing the probability to .4, and .5, and rework part a).

4) The vice president of a bank wishes to provide banking services so that the probability of the number of waiting customers being greater than 8 is less than .07. Would this condition be satisfied if the number of waiting customers is a Poisson random variable with a mean of 5? Justify your answer with appropriate calculations.

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