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Which formula correctly gives the variance of a discrete random variable $X$?
A$V(X)=E(X^2)-[E(X)]^2$
B$V(X)=E(X^2)+[E(X)]^2$
C$V(X)=E(X)-E(X^2)$
D$V(X)=[E(X)]^2-E(X)$
Answer & Solution
Correct answer: A. $V(X)=E(X^2)-[E(X)]^2$
The variance measures spread about the mean and is given by $V(X)=E(X^2)-[E(X)]^2$. This is equivalent to $\sum x_i^2p_i-\left(\sum x_ip_i\right)^2$.
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