U FUIIILD Suppose that X and Y are independent random variables with (1 20-1/2, t 1/2. (a) (2 points) Find M x+y(t). (b) (4 points) Find E[(X + Y)2]. Q Please select file(s) Select file(s} 09 Problem 7 (long answer) 8 Points Dr. McKinley orders a box of 2000 fair six-sided dice. She opens the box and dumps all the dice on the floor. Let X be the number of sixes that are rolled. (a) (3points) Identify the probability distribution ofX by name. What are its mean and variance? (b) (5 points) Use the Central Limit Theorem to approximate the probability of rolling between 300 and 400 sixes. Express your answer in terms of the normal CDF