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For independent random variables X and Y, the variance of their sum or difference is the sum of their variances:
Variances are added for both the sum and difference of two independent random variables because the variation in each variable contributes to the variation in each case. If the variables are not independent, then variability in one variable is related to variability in the other. For this reason, the variance of their sum or difference may not be calculated using the above formula
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Standard Deviation Puzzles - 3
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For independent random variables X and Y, the variance of their sum or difference is the sum of their variances:
Variances are added for both the sum and difference of two independent random variables because the variation in each variable contributes to the variation in each case. If the variables are not independent, then variability in one variable is related to variability in the other. For this reason, the variance of their sum or difference may not be calculated using the above formula