Question

1. according to north carolina mutual life insurances mortality table, the probability that a 60 - year - old woman will die within one year is 0.05. if she buys a $10,000 one - year term policy for $600, what is nc mutuals expected gain or loss?

outcome
probability p(x)

Explanation:

Step1: Determine the two outcomes and their probabilities

• Outcome 1: The woman does not die. The insurance company's gain is the premium, \(x_1 = 600\). The probability \(P(x_1)=1 - 0.05=0.95\)
• Outcome 2: The woman dies. The insurance company's gain is \(x_2=600 - 10000=- 9400\). The probability \(P(x_2)=0.05\)

Step2: Calculate the expected value \(E(X)\)

The formula for the expected value of a discrete random variable is \(E(X)=\sum_{i = 1}^{n}x_iP(x_i)\)

$$
LATEXBLOCK0
$$

Answer:

The expected gain for NC Mutual is \(\$100\)