Exam 4: Discrete Random Variables and Probability Distributions

If the random variables X and Y are statistically independent,then their joint probability distribution function equals the product of the marginal probability distribution functions.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A small grocery store has two checkout lines available to its customers: a regular checkout line and an express checkout line.Customers with 5 or fewer items are expected to use the express line.Let X and Y be the number of customers in the regular checkout line and the express checkout line,respectively.Note that these numbers include the customers being served,if any.The joint probability distribution is given in the table below. -Find the marginal distribution of Y.What does this distribution tell you?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Suppose X and Y are two random variables with E(X)= 1.50,E(Y)= 0.55,E(XY)= 0.80,Var(X)= 0.25,and Var(Y)= 0.2475. -What is the value of Corr(X,Y)?

A perfect straight line sloping downward would produce a covariance value of -1.

Thirty percent of all households have a DVD player.If you select 20 houses at random,what is the probability that six or fewer of them have a DVD player?

Compare the results of finding the mean and standard deviation,of the total amount that this investor earns in one year from these four investments,assuming that the returns are independent of each other and are no longer independent of one another.Explain the differences in your answers.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A bank grants mortgages to 87% of all applicants.After the applicant gets approval,the bank sends an appraiser to evaluate the value of the property.The bank pays an appraiser a salary of $2000 a month plus $200 for each appraisal.Assume the bank gets 10 loan applications next month. -What is the expected value of the amount of money the bank will have to pay its appraiser?

The mean of a Poisson distribution,where λ is the average number of successes occurring in a specified interval,is .

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Suppose X and Y are two random variables with E(X)= 1.50,E(Y)= 0.55,E(XY)= 0.80,Var(X)= 0.25,and Var(Y)= 0.2475. -What is the value of Cov(X,Y)?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution. -The listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called a(n):

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees. -What is the probability that three of the trainees will still be employed at the end of nine months?

The variance of the sum of two random variables is the sum of their variances plus two times the covariance.

The probability of observing the specific sequence of discrete outcomes is arrived at by applying the:

The number of orders shipped to a supplier that are inaccurate each month is an example of a:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is the expected value of X?

If X and Y are random variables with E(X)= 5 and E(Y)= 8,then E(2X + 3Y)is:

In a class of 18 students,there are 7 males and 11 females.A subcommittee of five students will be formed from this class.What is the probability that the subcommittee contains more males than females?

On average,how many of these ten people would you expect to catch a cold?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The probability that a person catches a cold during the cold and flu season is 0.4.Assume that 10 people are chosen at random. -What is the probability that exactly four of them will catch a cold?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: In a recent survey of 300 teenagers,62% of the teenagers indicated that they had been to a movie within the past month.75% of those teenagers who had seen a movie also had gone out to dinner in the past month,while only 64% of the teenagers who had not seen a movie had been out to dinner in the past month.Define the random variables as follows: X = 1 if teenager had been to movie;X = 0 otherwise Y = 1 if teenager had been out to dinner;Y = 0 otherwise -Find the joint probability function of X and Y.