A player tosses two fair coins. He wins Rs. 5 | vedclass

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(A) Let $X$ be the random variable representing the winning amount.The sample space is $S = \{HH, HT, TH, TT\}$.$1$. For two heads $(HH)$, $X = 5$, $P

Vedclass · Accepted Answer

$1.1875$

Vedclass · Answer

(A) Let $X$ be the random variable representing the winning amount.The sample space is $S = \{HH, HT, TH, TT\}$.$1$. For two heads $(HH)$, $X = 5$, $P(X=5) = 1/4$.$2$. For one head $(HT, TH)$, $X = 3$, $P(X=3) = 2/4 = 1/2$.$3$. For no head $(TT)$, $X = 2$, $P(X=2) = 1/4$.Mean $E(X) = \sum x_i p_i = 5(1/4) + 3(1/2) + 2(1/4) = 1.25 + 1.5 + 0.5 = 3.25$.$E(X^2) = \sum x_i^2 p_i = 5^2(1/4) + 3^2(1/2) + 2^2(1/4) = 25/4 + 9/2 + 4/4 = 6.25 + 4.5 + 1 = 11.75$.Variance $Var(X) = E(X^2) - [E(X)]^2 = 11.75 - (3.25)^2 = 11.75 - 10.5625 = 1.1875$.

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X=x)$	$k$	$2k$	$3k$	$4k$	$4k$	$3k$	$2k$	$k$	$k$

$A$ player tosses two fair coins. He wins $Rs. 5$ if two heads appear, $Rs. 3$ if one head appears, and $Rs. 2$ if no head appears. The variance of the winning amount is:

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