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On page 9 it is written that two variables have the same expectation (E[X] = E[Y]) if and only if they are almost surely equal (P[X=Y]=1). However, we may have two random variables X, Y which have the same expectation, even the same distribution, but are almost surely not equal - take X~N(0,1) and Y=-X.
I believe you meant to write P[X=Y] = 1 => E[X] = E[Y].
The text was updated successfully, but these errors were encountered:
On page 9 it is written that two variables have the same expectation (E[X] = E[Y]) if and only if they are almost surely equal (P[X=Y]=1). However, we may have two random variables X, Y which have the same expectation, even the same distribution, but are almost surely not equal - take X~N(0,1) and Y=-X.
I believe you meant to write P[X=Y] = 1 => E[X] = E[Y].
The text was updated successfully, but these errors were encountered: