DevoreStat 3..024.32105 0/7 points An insurance company offers its policyholders a number of different premium payment options. For a randomly select policyholder, let X = the number of months between successive payments. The cdr of X is as follows: 0x<1 0.35 15x <3 0.47 38 x 4 F(x) = 0.50 45x6 0.85 65 x < 12 11 12 X (a) What is the pmf of X? (b) Using just the odt, compute P(3 sX s 6) and P(4 5 X). P(3 SXS 6) - 50 PX4 SX) . 4. 0/4 points DevoreStat 3.5.039. (4573613) A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 3-lb batches. Let x the number of batches ordered by a randomly chosen customer and suppose that X has the following pmf. 1 2 3 4 p(x) 0.3 0.5 0.1 0.1 Compute E(X) and V(X). E(X) = Z batches V[X) = 1(0:3)2(0.5) 0.1-10) (0.3) 2 (0.160.1) +0,1) 42 - 2 Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds left. (Hint: The number of pounds left is a linear function of X.] expected weight left lb variance of weight left 0/4 points DevareState 3.E.029. [4573358) The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. x 1 2 4 8 16 P(x) 0.05 0.20 0.25 0 .30 0.20 (a) Compute E(X). (Enter your answer to two decimal places.) TGB (b) Compute Vix) directly from the definition, (Enter your answer to four decimal places.) GB2 (c) Compute the standard deviation of X. (Round your answer to three decimal places.) GB (d) Compute Vix) using the shortcut formula. (Enter your answer to four decimal places.) GB