Let the random variable X represent the product of the number of dots facing up on each die after a pair of fair dice is rolled. Let Y represent the sum of the number of dots facing up on the pair of...

Let the random variable X represent the product of the number of dots facing up on each die after a pair of fair dice is rolled. Let Y represent the sum of the number of dots facing up on the pair of dice.

a. Define a probability model (R(X),f (x)) for the random variable X.

b. What is the probability that X
 16?

c. Define a probability model (R(X,Y),f(x,y)) for the random vector (X,Y).

d. What is the probability that X
 16 and Y
 8?

e. Are X and Y independent random variables?

f. Define the conditional PDF of X given that Y = 7.

g. What is the probability that X
 10 given that Y = 7?