Notes Ask Your Teache a $20,000, 1-year term-life Insurance policy for $450. Ass

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Notes Ask Your Teache a $20,000, 1-year term-life Insurance policy for $450. Assuming that the probability that he will live for another year is 0.989, find the company's expected gain. Need Help? Taik to Tutor My Notes Ask Your Teaches -5.5 points TanFin11 8/003. The probability distribution of a random variable X is shown in the following table. 0.1 0.3 0.1 0.2 0.1 0.2 (a) Compute P(1 s Xs 3). (b) Compute the mean and standard deviation of x. (Round your answers to two decimal places.) standard deviation Need Help? Tal to Tutor

Explanation / Answer

1) Expected gain = 0.989 * 450 - (1 - 0.989)*(20000 - 450) = 230

2) a) P(1 < X < 3) = P(X = 1) + P(X = 2) + P(X = 3)

                             = 0.3 + 0.1 + 0.2

                             = 0.6

b) mean = E(X) = 0 * 0.1 + 1 * 0.3 + 2 * 0.1 + 3 * 0.2 + 4 * 0.1 + 5 * 0.2 = 2.5

E(X2) = 02 * 0.1 + 12 * 0.3 + 22 * 0.1 + 32 * 0.2 + 42 * 0.1 + 52 * 0.2 = 9.1

Var(X) = E(X2) - (E(X))2 = 9.1 - 2.52 = 2.85

Standard deviation = sqrt(2.85) = 1.69

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