Let ZaXbY where X and Y are two discrete random variables while a and b are two

# Let zaxby where x and y are two discrete random

• 9

This preview shows page 5 - 9 out of 9 pages.

Let Z=aX+bY where X and Y are two discrete random variables while a and b are two constants. Using the formula for the expected value of a function of two discrete random variables (found on your cheat sheet), show that the variance of Z can be written as follows: Var(Z)=a 2 Var(X)+ b 2 Var(Y)+2abCov(X,Y) (10 points) Subscribe to view the full document. Question 5 The following table presents the joint probability distribution of two discrete random variables X and Y. X 1 2 3 0 0.10 0.21 0.06 Y 1 0.05 0.10 0.11 2 0.02 0.11 0.24 a) Graph the conditional probability distribution of X given Y = 2 as a function of x. (6 points) b) Graph the cumulative probability function of Y as a function of y. (6 points) Subscribe to view the full document.

c) Calculate the correlation coefficient between X and Y. (10 points) Bonus : Using the definition of the expectation of a discrete random variable, show that the variance of a binomial distribution is np(1-p). (5 points) • Fall '16

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern