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A fair coin is tossed 2 times. A person receives $₹ X^{3}$ if he gets $X$ number of heads.
His expected gain is $=$
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His expected gain is $=$
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Verified Answer
The correct answer is:
$₹ 2.50$
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.
$$
\begin{aligned}
\therefore \text { Expected gain } &=\left(\frac{1}{4} \times 0\right)+\left(\frac{1}{2} \times 1^{3}\right)+\left(\frac{1}{4} \times 2^{3}\right) \\
&=0+\frac{1}{2}+\frac{8}{4}=2.5
\end{aligned}
$$
$$
\therefore P(X=0)=\frac{1}{4}, P(X=1)=\frac{2}{4}=\frac{1}{2}, P(X=2)=\frac{1}{4}
$$
Given a person receives $₹ X^{3}$ if we gets $X$ no. of heads.
$$
\begin{aligned}
\therefore \text { Expected gain } &=\left(\frac{1}{4} \times 0\right)+\left(\frac{1}{2} \times 1^{3}\right)+\left(\frac{1}{4} \times 2^{3}\right) \\
&=0+\frac{1}{2}+\frac{8}{4}=2.5
\end{aligned}
$$
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