Exam 4: Discrete Random Variables and Probability Distributions

From a group of 10 bank officers,3 are selected at random to be relocated and supervise new branch offices.If two of the 10 officers are women and 8 are men,what is the probability exactly one of the officers to be relocated will be a woman?

A continuous random variable is a random variable if it can take on no more than a countable number of values.

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time,space,or distance is very small.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A computer store receives a shipment of 14 computers,5 of which already have modems installed.Unfortunately,the boxes are not labeled so you are unsure which computers have modems.Assume you select 4 computers. -What is the probability that exactly two of them have modems?

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. -What is the probability that there are exactly four calls during the next ten minutes?

One of the required properties of a probability distribution function for a discrete random variable X is that .

If X and Y are independent random variables,which of the following identities is false?

Find the probability that at most 4 children do not recognize their mother's voice?

A Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

In the case where two or more,possibly related,discrete random variables are examined,it is important that probability models reflect the joint effect of variables on probabilities.

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 Var(2X - 3Y)?

The following table displays the joint probability distribution of X and Y.What is the covariance between the X and Y?

Calculate E(X + Y)and Var(X + Y)directly by using the probability distribution of X + Y.

Show that Var(X + Y)= Var(X)+ Var(Y).Did you expect this result? Why?

A discrete random variable is a random variable if it can take on an infinite number of values.

The binomial and the hypergeometric probability distributions are examples of discrete probability distributions.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table displays the joint probability distribution of two discrete random variables X and Y. -Compute the expected value for X.