Exercise · ZW-EXPECTED-VALUE-008 · ★★☆ Intermediate
\(X\) equals \(-1\), 0 or 1 with probabilities \(\tfrac14,\tfrac12,\tfrac14\). Compute \(E[X^2]\).
Choose one option.
Show answer
- D. \(\dfrac{1}{2}\)
Explanation
\(E[X^2]=1\cdot\tfrac14+0\cdot\tfrac12+1\cdot\tfrac14=\tfrac12\). The value 0 is \((E[X])^2\), since \(E[X]=0\).
Review the concept: Expected value
The expectation \(E[X]\) of a random variable \(X\) is the average of its possible values, each weighted by its probability.
\[\begin{aligned}E[X]&=\sum_x x\,p(x)\\ E[X]&=\int_{-\infty}^{\infty}x\,f(x)\,dx\end{aligned}\]
More practice problems: expected value
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