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Variance of a Discrete Random Variable

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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 σ2=∑x2⋅p(x)\sigma^2 = \sum x^2 \cdot p(x) without subtracting the mean.

B

The variance is calculated as σ2=(∑x⋅p(x))2\sigma^2 = \Big(\sum x \cdot p(x)\Big)^2.

C

The variance is calculated as σ2=∑(x−μ)2⋅p(x)\sigma^2 = \sum (x - \mu)^2 \cdot p(x), summing over all outcomes.

D

The variance is calculated as σ2=∑(x−μ)⋅p(x)\sigma^2 = \sum (x - \mu) \cdot p(x).

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