VIPSolutionsThe annual premium for a $15,000 insurance policy against the theft of a painting is $250. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Co Let X be the random variable for the amount of money received from the insurance company in the given year. E(X)=| | dollars
Question:
The annual premium for a $15,000 insurance policy against the theft of a painting is $250. If the (empirical) probability that
the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out
this insurance?
Co
Let X be the random variable for the amount of money received from the insurance company in the given year.
E(X)=| | dollars
This is AI generated Response.
Asked by: nayan
Created at: 2025-09-14 17:15:49
Asked by: nayan
Created at: 2025-09-14 17:15:49
Final Answer:
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Let's break down the problem:
- **Insurance payout if painting is stolen:** $15,000
- **Probability painting is stolen:** 0.02
- **Probability painting is NOT stolen:** 1 - 0.02 = 0.98
- **Annual premium (amount you pay):** $250
Let \( X \) be the amount received **from the insurance company** in a year:
- If stolen: receive $15,000 from insurance
- If not stolen: receive $0 from insurance
### Expected Value Calculation
\[
E(X) = (15000 \times 0.02) + (0 \times 0.98)
\]
\[
E(X) = 300 + 0 = 300
\]
So,
\[
\boxed{300} \text{ dollars}
\]
is the expected return from the insurance company in a given year.
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