Exam 4: Discrete Random Variables and Probability Distributions

Consider the following game.You choose a number from 1 to 6 and pay $1 to roll three dice.If your number is rolled on any of the dice,you get your dollar back and one dollar for each of the times your number came up.For instance,if your number comes up on two of the three dice,than you get a total of three dollars back.On average,how much would you expect to win at this game?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. -What is the expected number of pieces of junk mail you receive daily?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box.A sample of boxes results in the following table. -What is the standard deviation of the weight of cereal in the boxes?

Computation of marginal probabilities,means,and variances for jointly distributed random variables cannot be developed using a computer package.

If the correlation coefficient r = 0,then there is no relationship whatsoever between the two random variables.

Thirty percent of all households have a DVD player.Suppose you select 20 houses at random.On average,how many houses of the twenty would you expect to have a DVD? What is the standard deviation of the number of houses with a DVD?

If X and Y are two variables with = 3.25, = 5.8,and Cov(X,Y)= 14.703,then the coefficient of correlation p = 0.78.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activities.The following output was generated using Minitab: Covariances Let X = weekly take-home pay,and Y = amount spent weekly on recreational activities. -Identify the covariance between X and Y.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: 70% of the customers at the local ice cream shop order their ice cream on a sugar cone.Assume that the next ten customers order independently of one another. -What is the probability that more than half of them order sugar cones?

Which of the following is an example of a discrete random variable?

The sum of Poisson random variables is also a Poisson random variable.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws. -What is the standard deviation of the number of free throws that he will make?

If the number of possible outcomes of a random variable is infinite but countable,the random variable is considered discrete.

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 no more than two of them have modems?

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 can you say about the relationship between X and Y?

Let the random variable X denote the number of children who do not recognize their mother's voice.Find the mean of X.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency. -What is the average number of claims processed?

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 mean for the linear function W = 2X + Y.

The approach,to develop the binomial probability distribution,begins with the:

Now,assume that the returns of the four stocks are no longer independent of one another.Specifically,the correlations between all pairs of stock returns are given in the table below. Find the mean and standard deviation of the total amount that this investor earns in one year from these four investments.