Let R be the visual acuity readings for the right eye of a randomly selected person and L be the corresponding visual acuity readings for the left eye. It was found that the standard deviation of the right eye readings was 0.2 and the standard deviation of the left eye readings was 0.1. The standard deviation of the difference in visual acuity readings (R - L) is: I took sqrt of var(R)+var(L) and got 0.224 as the answer but that's incorrect. Would appreciate some help!
2026-04-02 11:09:47.1775128187
Standard deviation transformations
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The equation $\text{Var} [X - Y] = \text{Var}[X] + \text{Var}[Y]$ is only true if $X$ and $Y$ are independent, which is likely not true here because the variables are very likely dependent. Intuitively, if we know one eye is good then the other is probably more likely to be good, and vice versa.
The general identity is $\text{Var}[X-Y] = \text{Var}[X] + \text{Var}[Y] - 2 \text{Cov}[X,Y],$ which we cannot use here without knowing the covariance between the two variables. So, we need more information.