Independent solution

How to solve this Discrete Payment Variance question

Setup

Setup

List the four possible policy payments and their probabilities. The probabilities sum to one, so the first two raw moments can be computed directly.

Pr⁡(Y=0,300,600,700)=(0.72,0.14,0.06,0.08)\Pr(Y=0,300,600,700)=(0.72,0.14,0.06,0.08)

Model

Model

The probability-weighted payment values give mean 134, while the probability-weighted squared payments give second moment 73,400.

E[Y]=134,E[Y2]=73,400E[Y]=134,\quad E[Y^2]=73{,}400

Compute

Compute

Subtracting the squared mean from the second moment gives variance 55,444. Its square root is approximately 235.465.

SD⁡(Y)=73,400−1342=55,444=235.465\operatorname{SD}(Y)=\sqrt{73{,}400-134^2}=\sqrt{55{,}444}=235.465

Answer

Answer

The policy payment standard deviation rounds to 235.

235(B)\boxed{235\quad\text{(B)}}