Exam 4: Discrete Random Variables and Probability Distributions

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: In an office of 18 people,there are 7 men and 11 women.A subcommittee of four people will be formed from this group. -What is the probability that the subcommittee contains two men and two women?

In a box of 20 chocolates,there are four chocolates with coconut filling.What is the probability of choosing four chocolates,one or more of which have coconut filling?

If X and Y are random variables with Var(X)= 7.5,Var(Y)= 6 and Cov(X,Y)= 4,then Var(2X + 3Y)is:

A perfect straight line sloping upward would produce a correlation coefficient value of +1.

The number of males selected from a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.

How do the mean and standard deviation of the total amount that this investor earns in one year change as the $60,000 in cash available is reallocated for investment? Provide an intuitive explanation for the changes you observed here.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -Which of the following is true for the binomial distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The quality of computer disks is measured by sending the disks through a certifier which counts the number of missing pulses.A certain brand of computer disks averages 0.1 missing pulse per disk.Let the random variable X denote the number of missing pulses. -What is the distribution of X?

Are X and Y independent? Explain.

If X and Y are any random variables with Cov(X,Y)= 0.25, = 0.36,and = 0)49,then the coefficient of correlation p is:

Which of the following is an example of a binomial experiment?

Develop a realistic example of a pair of random variables for which you would expect to find negative covariance.

The number of customers that are served at a fast food restaurant between noon and 2:00 p.m.is an example of a discrete random variable.

The mean and variance of the Poisson distribution are equal.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: It has been reported that 1.7% of the work force will retire this year.Consider a random sample of 200 workers. -What is the probability that more than three of them will retire this year? Use the Poisson approximation to the binomial.

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 variance of the amount of money the bank will have to pay its appraiser?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: From past experience,it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female.A random sample of 20 one-year-olds is given this voice recognition test. -Find the probability all 20 children recognize their mother's voice.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table displays the joint probability distribution of two discrete random variables X and Y. -Determine the marginal probability distribution for 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 exactly seven of them order sugar cones?

The cumulative probability function for a random variable X expresses the probability that X exceeds the value of x₀,as a function of x₀.