(Solved): 7. [6+4+6 = 16 pts] (Probability) Suppose that 10 fair dice are rolled. Define the random variables ...

7. [6+4+6 = 16 pts] (Probability) Suppose that 10 fair dice are rolled. Define the random variables: X = number of times 3 appears, Y = number of elements from {1, 2, 3, 4, 5, 6) that never appear, and for i=1,2,3,4,5,6 Y? = 1, if i never appears otherwise. (a) Write down the probability distribution for X and calculate E(X). (b) Write down the probability distribution for Y? and calculate E(Y?). (c) Calculate E(Y). Show all your steps clearly.