A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The company collects a premium of $250 each year as payment for the insurance. The amount X that the company earns on this policy is $250 per year, less the $100,000 that it must pay if the insured dies. From mortality tables, the expected value of X, denoted E(X) or ?, is $304 and the standard deviation of X, denoted SD(X) or ?, is $9002. Question 1. The risk of insuring one person's life is reduced if we insure many people. Suppose an insurance company insures two 21-year-old males and that their ages at death are independent. If X1 and X2 are what the company earns from the two insurance policies, the insurance company's average income on the two policies is Z = 1/2 (X1 + X2) Find the expected value E(Z) and the standard deviation SD(Z) of the random variable Z. (Note: since the ages at death are independent, Var(X1+X2)=Var(X1)+Var(X2)) 2. If four 21-year-old males are insured, the insurance company's average income is where Xi is what the insurance company earns by insuring one man. The Xi are independent and each has the same distribution with expected value E(X) and standard deviation SD(X) as given above. Find the expected value E(Z) and the standard deviation SD(Z) of the random variable Z.
A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The company collects a premium of $250 each year as payment for the insurance. The amount X that the company earns on this policy is $250 per year, less the $100,000 that it must pay if the insured dies. From mortality tables, the
Question 1. The risk of insuring one person's life is reduced if we insure many people. Suppose an insurance company insures two 21-year-old males and that their ages at death are independent. If X1 and X2 are what the company earns from the two insurance policies, the insurance company's average income on the two policies is Z = 1/2 (X1 + X2)
Find the expected value E(Z) and the standard deviation SD(Z) of the random variable Z. (Note: since the ages at death are independent, Var(X1+X2)=Var(X1)+Var(X2))
2. If four 21-year-old males are insured, the insurance company's average income is where Xi is what the insurance company earns by insuring one man. The Xi are independent and each has the same distribution with expected value E(X) and standard deviation SD(X) as given above.
Find the expected value E(Z) and the standard deviation SD(Z) of the random variable Z.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
