Question

Laverny tosses an unbiased coin. He receives P100 if a head appears and he pays P40 it a tail appears Find the expected value and the variance of his gain.

Answer 1

Let X= the amount of money which Laverny receives.

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

(a) Expected value $=E[X]$

$=0.5(100)+0.5(-40)=30$

(b) Variance

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

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

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