Compute the Variance and Standard Deviation of a Discrete Random Variable
-The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable $x$.
$\begin{array}{c|c}
\mathrm{x} & \mathrm{P}(\mathrm{x}) \
\hline 0 & 0.49 \
1 & 0.05 \
2 & 0.32 \
3 & 0.07 \
4 & 0.07
\end{array}$

A) mean: 1.18; standard deviation: $1.30$
B) mean: 1.39; standard deviation: $0.64$
C) mean: $1.39$; standard deviation: $0.80$
D) mean: $1.18$; standard deviation: $0.64$

Question

Compute the Variance and Standard Deviation of a Discrete Random Variable
-The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable $x$.
$\begin{array}{c|c}
\mathrm{x} & \mathrm{P}(\mathrm{x}) \
\hline 0 & 0.49 \
1 & 0.05 \
2 & 0.32 \
3 & 0.07 \
4 & 0.07
\end{array}$

A) mean: 1.18; standard deviation: $1.30$
B) mean: 1.39; standard deviation: $0.64$
C) mean: $1.39$; standard deviation: $0.80$
D) mean: $1.18$; standard deviation: $0.64$

Quizplus · Accepted Answer

To calculate the mean ($\mu$), multiply each value of $x$ by its probability and sum these products: $\mu = (0)(0.49) + (1)(0.05) + (2)(0.32) + (3)(0.07) + (4)(0.07) = 1.18$. For the variance ($\sigma^2$), use the formula $\sigma^2 = \sum [x^2P(x)] - \mu^2$, then calculate the standard deviation ($\sigma$) as the square root of the variance. The calculations yield a variance of $1.69$ and a standard deviation of approximately $1.30$.

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