A random variable X has the following probabi | vedclass

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(D) Since the sum of probabilities is $1$:$\frac{1}{6} + k + \frac{1}{4} + k + \frac{1}{6} = 1$$2k + \frac{7}{12} = 1 \implies 2k = \frac{5}{12} \impl

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$\frac{7}{4}$

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(D) Since the sum of probabilities is $1$:$\frac{1}{6} + k + \frac{1}{4} + k + \frac{1}{6} = 1$$2k + \frac{7}{12} = 1 \implies 2k = \frac{5}{12} \implies k = \frac{5}{24}$Calculation for Variance:$\begin{array}{|c|c|c|c|} \hline x_i & P(X=x_i) & x_i P(x_i) & x_i^2 P(x_i) \ \hline -2 & 1/6 & -1/3 & 2/3 \ \hline -1 & 5/24 & -5/24 & 5/24 \ \hline 0 & 1/4 & 0 & 0 \ \hline 1 & 5/24 & 5/24 & 5/24 \ \hline 2 & 1/6 & 1/3 & 2/3 \ \hline 	ext{Total} & 1 & 0 & 21/12 \ \hline \end{array}$$	ext{Variance} = E(X^2) - [E(X)]^2$$= \frac{21}{12} - (0)^2 = \frac{7}{4}$

$X=x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X=x_i)$	$1/6$	$k$	$1/4$	$k$	$1/6$

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X=x)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

$A$ random variable $X$ has the following probability distribution:

$X=x_i$ $-2$ $-1$ $0$ $1$ $2$

$P(X=x_i)$ $1/6$ $k$ $1/4$ $k$ $1/6$

The variance of this random variable is

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$A$ random variable $X$ has the following probability distribution: $X=x_i$ $-2$ $-1$ $0$ $1$ $2$ $P(X=x_i)$ $1/6$ $k$ $1/4$ $k$ $1/6$ The variance of this random variable is