In each play of a certain casino game suppose you will win X where X is a random variable taking positive integer values with probability function f(x)= K\" forx=1,2,3,...,K Kx(x+ 1) Here K is the maximum payout that the casino will give on bets. 3. Find P(X2k),k=2,3,4,.... and the c.d.f. F(x). b. The expected value is a fair (a long-run break-even ) price one should charge for each play of this game. Find the expected value for a random variable with this probability function f(x). Approximate it a large value of K, K=1000O (you may use Calculus to do this). c. What is the value of E(X) if K = 00? (Hlnt: you might wish to take a limit)