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(A) The sample space of the experiment is $S = \{1, 2, 3, 4, 5, 6\}$.Let $X$ denote the number obtained on the throw. Then $X$ is a random variable wh

Vedclass · Accepted Answer

$\frac{35}{12}$

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(A) The sample space of the experiment is $S = \{1, 2, 3, 4, 5, 6\}$.Let $X$ denote the number obtained on the throw. Then $X$ is a random variable which can take values $1, 2, 3, 4, 5,$ or $6$.Since it is a fair die,$P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = \frac{1}{6}$.						$X$			$1, 2, 3, 4, 5, 6$							$P(X)$			$\frac{1}{6}, \frac{1}{6}, \frac{1}{6}, \frac{1}{6}, \frac{1}{6}, \frac{1}{6}$			Now,$E(X) = \sum x_i p(x_i) = (1+2+3+4+5+6) 	imes \frac{1}{6} = \frac{21}{6} = \frac{7}{2}$.Also,$E(X^2) = \sum x_i^2 p(x_i) = (1^2+2^2+3^2+4^2+5^2+6^2) 	imes \frac{1}{6} = (1+4+9+16+25+36) 	imes \frac{1}{6} = \frac{91}{6}$.Thus,$Var(X) = E(X^2) - (E(X))^2 = \frac{91}{6} - (\frac{7}{2})^2 = \frac{91}{6} - \frac{49}{4} = \frac{182 - 147}{12} = \frac{35}{12}$.

Find the variance of the number obtained on a throw of a fair die.

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