Let the independent random variable X and Y have binomial distributions with parameters 71;; = 2, px = p and It}; = 4,. p}; = p, respectively. If nor 2 1) = 5,\"; {a} [3 points] Please nd p and Pr(}' \"2 2). {b} [4 points] Please compute Pr[X = Y). {c} [4 points] Please compute Pr(X 2-: F). {d} [4 points] Please nd the mode of X and 1'. Are the distributions of X and Y right-skewed, left-skewed or symmetric? Toss a fair onedollar coin twice and a fair Fivedollar coin three times, respectively. Let X be the numbers of heads for one-dollar coin and Y be the numbers of heads forfivedollar coin. ie} [2 Points] What probability distribution {including its parameters} does Xfollow? What about F? (ii [3 Points] If we let random variable Z = X + Y, what's the Expectation value and variance of Z? (9} [6 Points] Could you please find out the Probability Mass Function (PMFJ of Z? {h} [2 Points] What probability distribution function does Z follow?| What conclusion can you draw based on the result? ii} [5 Points] If we let random variable W = X 1", Could you please find out the Probability Mass Function [PMFl of W? And what's the Expectation value and Variance of W