Complete parts a) - c) below. Be sure to show your work. 4) A local television s

Question

Complete parts a) - c) below. Be sure to show your work. 4) A local television statison sells 15-second, 30-second, and 60-second advertising spots Let x denote the length of a randomly selected commercial appearing on this station and suppose the probability distribution of x is given by the following: 15 0.1 30 0.3 p(x) a) Find E(X), E(x2). and Var (X) for this distribution. c) The price paid for commercials appearing on this station can be modeled by Y-0.296x2+33.33X+66.67 What is the average amount paid for commercials appearing on this station? 8

Explanation / Answer

a) E(X) = 15 * 0.1 + 30 * 0.3 + 60 * 0.6 = 46.5

E(X2) = 152 * 0.1 + 302 * 0.3 + 602 * 0.6 = 2452.5

Var(X) = E(X2) - (E(X))2 = 2452.5 - 46.52 = 290.25

b) E(Y) = -0.296 * E(X2) + 33.33 * E(X) + 66.67 = -0.296 * 2452.5 + 33.33 * 46.5 + 66.67 = 890.575

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