A fair coin is tossed 2 times. A person receives $₹ X^{3}$ if he gets $X$ number of heads. His expected gain…
A fair coin is tossed 2 times. A person receives $₹ X^{3}$ if he gets $X$ number of heads.
His expected gain is $=$
$₹ 2.00$
$₹ 1.00$
$₹ 2.50$
$₹ 5.20$
Solution
A fair coin is tossed 2 times. Possible outcomes are HH, HT, TH, TT $\therefore X$ takes values $0,1,2$
$\therefore P(X=0)=\frac{1}{4}, P(X=1)=\frac{2}{4}=\frac{1}{2}, P(X=2)=\frac{1}{4}$
Given a person receives $₹ X^{3}$ if we gets $X$ no. of heads.
$\begin{aligned}
\therefore \text { Expected gain } &=\left(\frac{1}{4} \times 0\right)+\left(\frac{1}{2} \times 1^{3}\right)+\left(\frac{1}{4} \times 2^{3}\right) \\
&=0+\frac{1}{2}+\frac{8}{4}=2.5
\end{aligned}$