If X is Uniform over (0,1), calculate E(X^n) and Var(X^n).
Please help
Definition: where f(x) is the pdf of X.
Therefore
Let .
.
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As an alternative to the above calculations, you could calculate the pdf of Y = X^n.
It's not hard to get for and zero otherwise.
Use it to calculate E(Y) and Var(Y).