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)

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)