Variance of sum and difference of random variables | Random variables | AP Statistics | Khan Academy

Intuition for why the variance of both the sum and difference of two independent random variables is equal to the sum of their variances.

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[luccacamillo]

A nice way to visualize Var(X - Y) is if you used the bowl to "scoop out" cereal from the box. Think that the "scoop quantity" varies in the same way a bowl of cereal would. Better yet, replace the cereal in the bowl with a sort-of-vacuum, empty space with varying "volume" that captures the cereal from the box. Well, the avg-quantity of the box+vacuum is lower than the box+bowl, but the variance is the same, since, in the bowl, the vaccum varies in the same way as the cereal.

[phiyahfit]

Oh wow I see!!!! Khan academy saves my life 😩

[suyashmuley]

Can you explain what the minimum and maximum variance be for sum of any n random variables? Here, it seems that you have chosen a special case for the deviations. Can it take the value as low as zero or as high as some fraction of the mean? Are there any such bounds imposed upon these values?

[哇咔咔-ev]

i have a question, what it will be if Var(2X-Y)?

[leylasuleymanli]

this video does not prove the E(X+Y) which u said u will prove it in the related previous video

[phiyahfit]

But why can’t you just add the standard deviations? So confusing