Mean of Sum of IID Random Variables

[ObliviousSage]

If X is some RV, and Y is a sum of n independent X_is (i.e. n independent identically distributed random variables with distribution X), is the mean of Y just the sum of the means of the n Xs?

That is, if Y=X₁+X₂+...+X_n, is E[Y]=nE[X]?

I know that for one-to-one order-preserving functions, if Y=h(X) then E[Y]=E[h(X)] with a single variable X, but I'm not sure if it works with multiple Xs, even with something as simple as addition.

 

[mathman]

The mean of a sum is the sum of the means. The terms in the sum do not have to be independent or have the same distribution.

 

[ObliviousSage]

The mean of a sum is the sum of the means. The terms in the sum do not have to be independent or have the same distribution.

Awesome, I wasn't sure. Thanks for clearing that up!