Chapter 6.1, Problem 18E

a.

To determine

To explain: The reason of selling insurance is not risky

Answer to Problem 18E

Because large number of risk holders are involved.

Explanation of Solution

Given:

Gain is $1250.

Amount lost in case of death is $100,000

Calculation:

The expected value can be computed as:

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum x\times P\left(x\right)}\\ =\left(-99750\right)\times 0.00183+\mathrm{....}+\left(1250\right)\times 0.99058\\ =303.35\end{array}$

Thus, the expected value is $303.35 per policy.

Risk is low because large number of policy holders are involved.

b.

To determine

To find: The standard deviation of Y.

Answer to Problem 18E

The standard deviation is $9708

Explanation of Solution

Calculation:

The standard deviation of Y can be calculated as:

  $\begin{array}{c}\sigma =\sqrt{{\displaystyle \sum x^2\times P\left(x\right)-{\left({\displaystyle \sum x\times P\left(x\right)}\right)}^2}}\\ =\sqrt{{\left(-99750-303.3525\right)}^2\times 0.00183+\mathrm{................}+{\left(1250-303.3525\right)}^2\times 0.99058}\\ =\$9708\end{array}$

Thus, the standard deviation is $9708.