APFIVE Variance of a Discrete Random Variable
For a discrete random variable with mean $\mu$ and probability distribution $p(x)$, which of the following is the correct formula for the variance, $\sigma^2$?
A
The variance is calculated as $$\sigma^2 = \Big(\sum x \cdot p(x)\Big)^2$$.
B
The variance is calculated as $$\sigma^2 = \sum x^2 \cdot p(x)$$ without subtracting the mean.
C
The variance is calculated as $$\sigma^2 = \sum (x - \mu)^2 \cdot p(x)$$, summing over all outcomes.
D
The variance is calculated as $$\sigma^2 = \sum (x - \mu) \cdot p(x)$$.
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