Estimate the variance for the following probability distribution to two decimal places. $$\begin{array} { c | c c c c }
x & 0 & 1 & 2 & 3 \
\hline \mathrm { P } ( x ) & 1 / 10 & 1 / 20 & 1 / 20 & 4 / 5
\end{array}$$
A) $2.55$
B) $0.95$
C) $0.97$
D) $0.90$
E)1.00

Question

Estimate the variance for the following probability distribution to two decimal places. $$\begin{array} { c | c c c c } 
x & 0 & 1 & 2 & 3 \
\hline \mathrm { P } ( x ) & 1 / 10 & 1 / 20 & 1 / 20 & 4 / 5
\end{array}$$
A) $2.55$
B) $0.95$
C) $0.97$
D) $0.90$
E)1.00

Quizplus · Accepted Answer

The variance of a probability distribution is calculated using the formula $\sigma^2 = \sum [x^2 \cdot P(x)] - \mu^2$, where $\mu$ is the mean of the distribution. First, calculate the mean: $\mu = (0)(1/10) + (1)(1/20) + (2)(1/20) + (3)(4/5) = 0 + 0.05 + 0.1 + 2.4 = 2.55$. Then, calculate the expected value of $x^2$: $E(x^2) = (0^2)(1/10) + (1^2)(1/20) + (2^2)(1/20) + (3^2)(4/5) = 0 + 0.05 + 0.2 + 7.2 = 7.45$. Finally, calculate the variance: $\sigma^2 = 7.45 - (2.55)^2 = 7.45 - 6.5025 = 0.9475$, which rounds to $0.95$.

Estimate the Variance for the Following Probability Distribution to Two x0123P(x)1/101/201/204/5\begin{array} { c | c c c c } x & 0 & 1 & 2 & 3 \\\hline \mathrm { P } ( x ) & 1 / 10 & 1 / 20 & 1 / 20 & 4 / 5\end{array}xP(x)​01/10​11/20​21/20​34/5​​

Estimate the Variance for the Following Probability Distribution to Two $\begin{array} { c | c c c c } x & 0 & 1 & 2 & 3 \\\hline \mathrm { P } ( x ) & 1 / 10 & 1 / 20 & 1 / 20 & 4 / 5\end{array}$