1. ## pdf and variance

Solved

2. []EDIT[]The interval was unspecified. Please check the interval on which the density is defined and put it in place of [a,b]

$E[Y]= \int_{a}^{b} y \times 3(1-y)^2 dy$

$E[Y^2]= \int_{a}^{b} y^2 \times 3(1-y)^2 dy$

Also, $Var(Y) = E[Y^2] - (E[Y])^2$

and, $Var(W) = 25Var(Y)$

Use:

http://integrals.wolfram.com/index.jsp

3. clearly the region isn't all of $R^1$ so that integration is incorrect