Q.1 Let X is the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has probability mass function X 13.5 15.9 19.1 P(X = x) 0.2 0.5 0.3 %3D (i) Verify that it is a...

Extracted text: Q.1 Let X is the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has probability mass function X 13.5 15.9 19.1 P(X = x) 0.2 0.5 0.3 %3D (i) Verify that it is a probability mass function. (ii) Find mean and standard deviation of above probability mass function. (iii) Find the probability that X is atleast 15. (iv) If the price of a freezer having capacity X cubic feet is 25X – 8.5, what is the expected price and variance paid by the next customer to buy a freezer? (v) Find moment generating function.