Problem 2: (Set Operations and Probability Equality) For two events A, B, dene C: (ADBC)U(BDAC) 1) We know that A F] B means both events occur and A U B means at least one of the two events occurs. In the same fashion, give a one-sentence interpretation of event C. 2) Show that 13(0) = P(A) + P(B) 2P(A n B) Problem 3: (Property of Exponential Distribution) We say that the distribution of random variable X follow exponential distribution With parameter A if: F(a,) = 1 e"'\" for a > 0 and F(a) = 0 for :c S 0. Prove the following results: for any s,t > 0, we have P(X > s + t) = P(X > s)P(X > t). Problem 4: (pmf and cdf) I toss a coin twice. Let X be the number of observed heads. (1) Find the cdf of X, and draw a plot for CDF. (2) Find the pmf of X