A person throws an unbiased die. If the numbe | vedclass

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(D) Let the random variable $X$ denote the gain or loss.When an unbiased die is thrown,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$,each with a pr

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(D) Let the random variable $X$ denote the gain or loss.When an unbiased die is thrown,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$,each with a probability of $\frac{1}{6}$.If the number is even,the gain is equal to the number shown $(X = x)$.If the number is odd,the loss is equal to the number shown $(X = -x)$.The probability distribution of $X$ is:$X = x$$-1$$2$$-3$$4$$-5$$6$$P(X = x)$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$$\frac{1}{6}$The expectation $E(X)$ is given by $\sum x \cdot P(X=x)$:$E(X) = (-1) \cdot \frac{1}{6} + 2 \cdot \frac{1}{6} + (-3) \cdot \frac{1}{6} + 4 \cdot \frac{1}{6} + (-5) \cdot \frac{1}{6} + 6 \cdot \frac{1}{6}$$E(X) = \frac{-1 + 2 - 3 + 4 - 5 + 6}{6}$$E(X) = \frac{3}{6} = 0.5$Thus,the expectation is ₹ $0.5$.

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

$A$ person throws an unbiased die. If the number shown is even,he gains an amount equal to the number shown. If the number is odd,he loses an amount equal to the number shown. Then his expectation is ₹.

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