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

question 17

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) \(\begin{array} { l l }
• \text { expected value (mean): } & - 1 \\
• \text { variance: } & 2 \\
• \text { standard deviation: } & 4
• \end{array}\)

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