If we randomly select four insured 21-year-old men, the insurer’s average income is

V = X₁ + X₂ + X₃ + X₄/4

where Xi is the income from insuring one man. Assuming that the amount of income earned on individual policies is independent, find the mean and standard deviation of V. (If you compare with the results of Exercise 63, you should see that averaging over more insured individuals reduces risk.)

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.

Exercise 63.

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