A fair coin is tossed 2 times. A person recei | vedclass

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(C) fair coin is tossed $2$ times. The sample space is $S = \{HH, HT, TH, TT\}$.Let $X$ be the number of heads. The possible values for $X$ are $0, 1,

Vedclass · Accepted Answer

$₹ 2.50$

Vedclass · Answer

(C) fair coin is tossed $2$ times. The sample space is $S = \{HH, HT, TH, TT\}$.Let $X$ be the number of heads. The possible values for $X$ are $0, 1, 2$.The corresponding probabilities are:$P(X=0) = \frac{1}{4}$$P(X=1) = \frac{2}{4} = \frac{1}{2}$$P(X=2) = \frac{1}{4}$The gain is given by $G(X) = X^{3}$.The expected gain $E[G(X)]$ is calculated as:$E[G(X)] = \sum P(X=x) \cdot G(x)$$E[G(X)] = (P(X=0) \cdot 0^{3}) + (P(X=1) \cdot 1^{3}) + (P(X=2) \cdot 2^{3})$$E[G(X)] = (\frac{1}{4} \cdot 0) + (\frac{1}{2} \cdot 1) + (\frac{1}{4} \cdot 8)$$E[G(X)] = 0 + 0.5 + 2 = 2.5$Thus,the expected gain is $₹ 2.50$.

$A$ 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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