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(A) To find the variance of the random variable $X$,we use the formula: $	ext{Var}(X) = E(X^2) - [E(X)]^2$.First,we calculate the mean $E(X) = \sum x

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$1.76$

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(A) To find the variance of the random variable $X$,we use the formula: $	ext{Var}(X) = E(X^2) - [E(X)]^2$.First,we calculate the mean $E(X) = \sum x_i P(x_i)$:$E(X) = (0 	imes 0.4) + (1 	imes 0.3) + (2 	imes 0.1) + (3 	imes 0.1) + (4 	imes 0.1)$$E(X) = 0 + 0.3 + 0.2 + 0.3 + 0.4 = 1.2$Next,we calculate $E(X^2) = \sum x_i^2 P(x_i)$:$E(X^2) = (0^2 	imes 0.4) + (1^2 	imes 0.3) + (2^2 	imes 0.1) + (3^2 	imes 0.1) + (4^2 	imes 0.1)$$E(X^2) = 0 + 0.3 + 0.4 + 0.9 + 1.6 = 3.2$Now,calculate the variance:$	ext{Var}(X) = E(X^2) - [E(X)]^2$$	ext{Var}(X) = 3.2 - (1.2)^2$$	ext{Var}(X) = 3.2 - 1.44 = 1.76$Thus,the variance of $X$ is $1.76$.

$X=x$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

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

The probability distribution of a random variable $X$ is given by
$X=x$ $0$ $1$ $2$ $3$ $4$
$P(X=x)$ $0.4$ $0.3$ $0.1$ $0.1$ $0.1$
The variance of $X$ is

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The probability distribution of a random variable $X$ is given by$X=x$$0$$1$$2$$3$$4$$P(X=x)$$0.4$$0.3$$0.1$$0.1$$0.1$The variance of $X$ is