The risk of insuring one person’s life is reduced if we insure many people. Suppose that we randomly select two insured 21 year-old males, and that their ages at death are independent. If X1 and X2 are the insurer’s income from the two insurance policies, the insurer’s average income W on the two policies is

W = X₁ + X₂/2

Find the mean and standard deviation of W. (You see that the mean income is the same as for a single policy, but the standard deviation is less.)

We examined the probability distribution of the random variable X = the amount a life insurance company earns on a randomly chosen 5-year term life policy. Calculations reveal that μX = $303.35 and σX = $9707.57.