Question

Dan tossed unbiased coin , on each toss he wins 50 pesos if head appears and losses 40 pesos if tail appears. What will be the expected value and variance of his gain?​

Answer 1

Since the coin is unbiased, the probability of getting a head or a tail is both $=0.5$

The expected value is thus

$=(50\times 0.5)-(40\times0.5)$

$= 5$ Pesos.

The variance

$\begin{matrix} x&P(x)&xP(x)&x^2P(x)\\-40&0.5&-20&800\\50&0.5&25&1250\\\sum &1&5&2050\end{matrix}$

$\sigma^2=\sum x^2P(x)-\sum (xP(x))^2$

$\sigma^2 =2050-25$

$\sigma^2=2025$