Question

Levie tosses an unbiased coin. He receives PHP 100 if a head appears and he pays PHP 40 is a tail appears. Find the expected value and the variance of his gain.

Answer 1

Let $X=$ the amount of money which Levie receives.

$$\begin{matrix} x & 100 & -40 \\ p(x) & 0.5 & 0.5 \end{matrix}$$

$$E[X]=0.5(100)+0.5(-40)=30$$

$$E[X^2]=0.5(100)^2+0.5(-40)^2=5800$$

$$V(X)=E[X^2]-(E[X])^2$$

$$=5800-(30)^2=4900$$