Find the Mean, Variance, and Standard Deviation of the Normal $f ( x ) = \frac { 1 } { 2 \sqrt { 2 \pi } } e ^ { - ( x -- 1 ) ^ { 2 }/8}$

Multiple Choice

Find the mean, variance, and standard deviation of the normal density function $f ( x ) = \frac { 1 } { 2 \sqrt { 2 \pi } } e ^ { - ( x -- 1 ) ^ { 2 }/8}$ over $( - \infty , \infty )$ . Do not use integration.

A) $\begin{array} { l l } \text { expected value(mean) : } & - 1 \\\text { variance: } & 4 \\\text { standard deviation: } & 2\end{array}$
B) $\begin{array} { l l } \text { expected value (mean) } ) : & 4 \\\text { variance: } & - 1 \\\text { standard dev iation: } & 2\end{array}$
C) $\begin{array} { l l } \text { expected value(mean } ) : & 4 \\\text { variance: } & 2 \\\text { standard dev iation: } & - 1\end{array}$
D) $\begin{array} { l l } \text { expected value (mean) : } & 2 \\\text { variance: } & - 1 \\\text { standard deviation: } & 4\end{array}$
E) $\begin{array} { l l } \text { expected value (mean) : } & - 1 \\\text { variance: } & 2 \\\text { standard deviation: } & 4\end{array}$