Physics · Advanced university
Variance of a two-outcome observable · formula reference
Compute the second moment before subtracting the square of the mean.
Formula
Compute the second moment before subtracting the square of the mean.
Var(A)=⟨A²⟩−⟨A⟩²
Worked example
An observable returns -6 with probability 0.2, and 8 otherwise. Calculate its quantum measurement variance. Round the final result to 4 decimal places if needed.
Compute ⟨A²⟩=0.2(-6²)+(1−0.2)(8²), then subtract [0.2(-6)+(1−0.2)(8)]².
31.36
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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