Exercise · ZW-NORMAL-DISTRIBUTION-008 · ★★☆ Intermediate
If \(Z\) is standard normal, what is \(E[Z^2]\)?
Choose one option.
Show answer
- D. \(1\)
Explanation
Since \(E[Z]=0\), \(E[Z^2]=\operatorname{Var}(Z)+E[Z]^2=1\).
Review the concept: Normal distribution
A normal variable is a continuous variable with density \(f\) shaped like a symmetric bell, determined by its mean \(\mu\) and its standard deviation \(\sigma\).
\[f(x)=\dfrac{1}{\sigma\sqrt{2\pi}}\,e^{-\frac{(x-\mu)^2}{2\sigma^2}}\]
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