Past exam of the computer science course of the University of Oxford / 2015 / Probability and computing / 1 / b

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- Solution b

Solution

For a real random variable

X

with finite expectation

μ = E X

, its variance is

Var (X) = E [(X - μ)^{2}] .

When the second moment is finite, expansion and linearity of expectation give

Var (X) = E [X^{2}] - μ^{2}

. The definition also permits infinite variance when the expectation is finite but the second moment is infinite.

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