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 paymen 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 μ, is $300 and the standard deviation of X, denoted SD(X) or o, is $9006. 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= + 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)) E(Z) = $ 300 SD(Z) = $12738.49 x. Question 2. If four 21-year-old males are insured, the insurance company's average income is Z = (X₁ + X₂ + X3 + X₁) where X, is what the insurance company earns by insuring one man. The X, 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. (Note: since the Xi's are independent, the variance of the sum of the Xi's is the sum of the individual variances). E(Z) = $ SD(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 paymen 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 μ, is $300 and the standard deviation of X, denoted SD(X) or o, is $9006. 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= + 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)) E(Z) = $ 300 SD(Z) = $12738.49 x. Question 2. If four 21-year-old males are insured, the insurance company's average income is Z = (X₁ + X₂ + X3 + X₁) where X, is what the insurance company earns by insuring one man. The X, 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. (Note: since the Xi's are independent, the variance of the sum of the Xi's is the sum of the individual variances). E(Z) = $ SD(Z) = $
Chapter6: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 8RE: Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25...
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Transcribed Image Text: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 μ,
is $300 and the standard deviation of X, denoted SD(X) or o, is $9006.
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
1/²7 ( X₁ + X₂)
2
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))
E(Z) $
=
300
Z =
SD(Z) = $12738.49 X
Question 2. If four 21-year-old males are insured, the insurance company's average income is
Z 1/7 (X₁ + X₂ + X3 + X₁)
4
where X; is what the insurance company earns by insuring one man. The X; 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. (Note: since the X;'s are independent, the variance of the sum of the X;'s is the sum of the individual variances).
E(Z) $
SD(Z) = $
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