The probability distribution of a random vari | vedclass

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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) = \su

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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 $1.76$.

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

The probability distribution of a random variable $X$ is given by:

$X=x$ $P(X=x)$

$0$ $0.4$

$1$ $0.3$

$2$ $0.1$

$3$ $0.1$

$4$ $0.1$

The variance of $X$ is:

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