Questions: If we let X be the profit of the insurance company from selling the insurance policy then the expected value of X is always negative. True False

If we let X be the profit of the insurance company from selling the insurance policy then the expected value of X is always negative.
True
False

Transcript text: Question 1 1 pts If we let X be the profit of the insurance company from selling the insurance policy then the expected value of $X$ is always negative. True False

Solution

Solution Steps

To determine whether the expected value of $ X $ is always negative, we need to consider the basic principle of insurance. Insurance companies set premiums such that, on average, they make a profit. This means that the expected value of the profit $ X $ should be positive, not negative. Therefore, the statement is false.

Step 1: Understanding the Expected Value

The expected value of a random variable $ X $ represents the average outcome of that variable over many trials. In the context of an insurance company, $ X $ represents the profit from selling insurance policies. The company sets premiums based on the expected payouts, aiming to ensure that the expected profit is positive.

Step 2: Analyzing the Statement

The statement claims that the expected value of $ X $ is always negative. However, insurance companies typically calculate premiums to cover expected claims and generate profit. Therefore, the expected value $ E[X] $ is generally positive, contradicting the statement.

Step 3: Conclusion

Since the expected value of the profit $ X $ is not always negative, we conclude that the statement is false.