Physics · Advanced university
Variance of a two-outcome observable
Compute the second moment before subtracting the square of the mean.
Method and conditions
Compute the second moment before subtracting the square of the mean.
Var(A)=⟨A²⟩−⟨A⟩²
Worked examples
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
An observable returns -1 with probability 0.4, and 14 otherwise. Calculate its quantum measurement variance. Round the final result to 4 decimal places if needed.
Compute ⟨A²⟩=0.4(-1²)+(1−0.4)(14²), then subtract [0.4(-1)+(1−0.4)(14)]².
54
Try it
An observable returns -1 with probability 0.3, and 3 otherwise. Calculate its quantum measurement variance. Round the final result to 4 decimal places if needed.
An observable returns 0 with probability 0.7, and 12 otherwise. Calculate its quantum measurement variance. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 3.36
Compute ⟨A²⟩=0.3(-1²)+(1−0.3)(3²), then subtract [0.3(-1)+(1−0.3)(3)]².
- 30.24
Compute ⟨A²⟩=0.7(0²)+(1−0.7)(12²), then subtract [0.7(0)+(1−0.7)(12)]².
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