Find the mean, variance, and standard deviation of the uniform distribution $f ( x ) = \frac { 1 } { 18 }$ over the interval [0, 18] without using integration.
A) $\begin{array} { l l }
\text { expected value (mean) : } & 9.000 \
\text { variance: } & 27.000 \
\text { standard deviation: } & 5.196
\end{array}$
B) $\begin{array} { l l }
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 5.196
\end{array}$
C) $\begin{array} { l l }
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 9.000
\end{array}$
D) $\begin{array} { l l }
\text { expected value (mean) } : & 5.196 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 27.000
\end{array}$
E) $\begin{array} { l l }
\text { expected value (mean) } & 9.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 27.000
\end{array}$

Question

Find the mean, variance, and standard deviation of the uniform distribution $f ( x ) = \frac { 1 } { 18 }$ over the interval [0, 18] without using integration.
A) $\begin{array} { l l } 
\text { expected value (mean) : } & 9.000 \
\text { variance: } & 27.000 \
\text { standard deviation: } & 5.196
\end{array}$
B) $\begin{array} { l l } 
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 5.196
\end{array}$
C) $\begin{array} { l l } 
\text { expected value (mean) : } & 27.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 9.000
\end{array}$
D) $\begin{array} { l l } 
\text { expected value (mean) } : & 5.196 \
\text { variance: } & 9.000 \
\text { standard deviation: } & 27.000
\end{array}$
E) $\begin{array} { l l } 
\text { expected value (mean) } & 9.000 \
\text { variance: } & 5.196 \
\text { standard deviation: } & 27.000
\end{array}$

Quizplus · Accepted Answer

For a uniform distribution over an interval [a, b], the mean (expected value) is $\frac{a + b}{2}$, the variance is $\frac{(b - a)^2}{12}$, and the standard deviation is the square root of the variance. Here, $a = 0$ and $b = 18$, so the mean is $9$, the variance is $27$, and the standard deviation is approximately $5.196$.

Find the Mean, Variance, and Standard Deviation of the Uniform f(x)=118f ( x ) = \frac { 1 } { 18 }f(x)=181​

Find the Mean, Variance, and Standard Deviation of the Uniform $f ( x ) = \frac { 1 } { 18 }$