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) = $
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
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) = $
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 8 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON