Originally Posted by
mr fantastic 1. Let $\displaystyle X = U + 1$.
The cdf of X is given by
$\displaystyle F(x) = \Pr(X < x) = \Pr(U + 1 < x) = \Pr(U < x - 1) = \int_{0}^{x - 1} 1 \, du = \, ....$
Therefore the pdf of X is given by $\displaystyle f(x) = \frac{dF}{dx} = \, .... $ for $\displaystyle 1 \leq x \leq 2$ and zero elsewhere.
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2. Let $\displaystyle Y = U^2$.
The cdf of Y is given by
$\displaystyle G(y) = \Pr(Y < y) = \Pr(U^2 < y) = \Pr(-\sqrt{y} < U < \sqrt{y}) = \int_{0}^{\sqrt{y}} 1 \, du = \, ....$
Therefore the pdf of Y is given by $\displaystyle g(y) = \frac{dG}{dy} = \, .... $ for $\displaystyle 0 \leq y \leq 1$ and zero elsewhere.