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[]EDIT[]The interval was unspecified. Please check the interval on which the density is defined and put it in place of [a,b]
$\displaystyle E[Y]= \int_{a}^{b} y \times 3(1-y)^2 dy$
$\displaystyle E[Y^2]= \int_{a}^{b} y^2 \times 3(1-y)^2 dy$
Also, $\displaystyle Var(Y) = E[Y^2] - (E[Y])^2$
and, $\displaystyle Var(W) = 25Var(Y)$
Use:
http://integrals.wolfram.com/index.jsp
to speed up your integration.
Anonymous