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(D) Step $1$: Calculate the mean $E(X) = \sum x_i P(x_i) = (0 	imes 0.3) + (1 	imes 0.4) + (2 	imes 0.3) = 0 + 0.4 + 0.6 = 1.0$.Step $2$: Calculate

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$0.7$

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(D) Step $1$: Calculate the mean $E(X) = \sum x_i P(x_i) = (0 	imes 0.3) + (1 	imes 0.4) + (2 	imes 0.3) = 0 + 0.4 + 0.6 = 1.0$.Step $2$: Calculate $E(X^2) = \sum x_i^2 P(x_i) = (0^2 	imes 0.3) + (1^2 	imes 0.4) + (2^2 	imes 0.3) = 0 + 0.4 + 1.2 = 1.6$.Step $3$: Calculate the variance $Var(X) = E(X^2) - [E(X)]^2 = 1.6 - (1.0)^2 = 1.6 - 1.0 = 0.6$.Step $4$: Calculate the standard deviation $\sigma = \sqrt{Var(X)} = \sqrt{0.6} \approx 0.77$. Since the closest option is $0.7$, we select $D$.

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

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

For the following probability distribution, the standard deviation of the random variable $X$ is:
$X: 0, 1, 2$
$P(X): 0.3, 0.4, 0.3$

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For the following probability distribution, the standard deviation of the random variable $X$ is:$X: 0, 1, 2$$P(X): 0.3, 0.4, 0.3$