Question 1:

Consider a random variable with the following pmf:

f(x) = c/6.24^x, where x = 0, 1, 2, 3. Find m = E(X).

Question 2:

Consider a random variable with the following pmf: c/ 3.14^{x ,}where x = 0, 1, 2, 3.

Question 3:

In a game, you first toss a coin. If the coin lands on head, you pull a slot machine once. If the coin lands on head, you pull a slot machine twice. The slot machine has a winning probability of 0.66, and you get $5 for every slot machine win. Let Y be the amount that you get paid. Find the expectation of Y.