Fill in the probability distribution table and find the expected value. 10) A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? 10) P(x)
Fill in the probability distribution table and find the expected value. 10) A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy? 10) P(x)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Probability Distribution and Expected Value Calculation**
A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. The probability that he will live through the year is 0.9994. What is the expected value for the insurance policy?
**Probability Distribution Table:**
| x | P(x) |
|---------|-------|
| | |
| | |
To find this expected value, the table needs to be filled with relevant data.
The possible outcomes (x) and their probabilities (P(x)) can be considered as:
1. The man survives the year and the insurance company keeps the premium:
- x = -$181 (loss for the man, the insurance keeps the premium)
- P(x) = 0.9994
2. The man does not survive the year, and the insurance company pays the coverage:
- x = $150,000 - $181 = $149,819 (gain for the man’s beneficiaries)
- P(x) = 1 - 0.9994 = 0.0006
The expected value (EV) of the insurance policy can be calculated as follows:
\[
EV = (x_1 \times P(x_1)) + (x_2 \times P(x_2))
\]
Substitute the values:
\[
EV = (-181 \times 0.9994) + (149,819 \times 0.0006)
\]
This will yield the expected monetary value for the policy from the perspective of the insurance customer (the man).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fe73833-ff5a-4353-be1d-d2c3741e990b%2F8f375076-5d8d-405a-a82f-ab22c81608d7%2F7wnei0p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability Distribution and Expected Value Calculation**
A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. The probability that he will live through the year is 0.9994. What is the expected value for the insurance policy?
**Probability Distribution Table:**
| x | P(x) |
|---------|-------|
| | |
| | |
To find this expected value, the table needs to be filled with relevant data.
The possible outcomes (x) and their probabilities (P(x)) can be considered as:
1. The man survives the year and the insurance company keeps the premium:
- x = -$181 (loss for the man, the insurance keeps the premium)
- P(x) = 0.9994
2. The man does not survive the year, and the insurance company pays the coverage:
- x = $150,000 - $181 = $149,819 (gain for the man’s beneficiaries)
- P(x) = 1 - 0.9994 = 0.0006
The expected value (EV) of the insurance policy can be calculated as follows:
\[
EV = (x_1 \times P(x_1)) + (x_2 \times P(x_2))
\]
Substitute the values:
\[
EV = (-181 \times 0.9994) + (149,819 \times 0.0006)
\]
This will yield the expected monetary value for the policy from the perspective of the insurance customer (the man).
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