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Mean of sum and difference

The mean of sum and difference of a discrete random variable is simply adding and subtracting.



Examples calculating mean of sum and difference

Intro-example: Let X be the colleagues that I greet on regular days at the office. The expected value of X is therefore the number of times that I am expected to greet a colleague on a regular day at the office and is denoted E(X) which is the same as the mean denoted with µ.


Sum of means

Say we have a number of outlets and we want to estimate the number of sales of a given product for tomorrow. Say that outlet X sales at average 3 unit of this product and that the expected value for number of sales of this product for outlet Y is 4.

What number of sales can we expect tomorrow for this product in outlet X and Y?

mean of sum and difference


Mean of difference

The same, as in the case above for addition, goes for subtraction: If we want to know how much more we can expect outlet B will sell tomorrow compared to outlet A, we subtract 3 from 4:

mean of sum and difference


Mean of sum and difference endnote

As such taking the mean of a sum and of a difference is fairly simple, but I include this as it helps me understanding the structure and notations for further calculations of other values like variance, etc.


Learning resources

Khan Academy video: Mean of sum and difference of random variables



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