I really do not understand this question. Could anyone point me in the right direction?
Thanks
Here is a start:
(a) The cdf of Y is:
$\displaystyle \displaystyle G(y) = \Pr(Y \leq y) = \Pr(aX + b \leq y) = \Pr\left(X \leq \frac{y - b}{a}\right)$ (assuming a > 0)
$\displaystyle \displaystyle = \int_{-\infty}^{\frac{y - b}{a}} f(x) \, dx$ where f(x) is the pdf of x.
Therefore the pdf of Y is:
$\displaystyle \displaystyle g(y) = \frac{d G}{dy} = f\left( \frac{y - b}{a}\right) \cdot \frac{1}{a}$ using the Fundamental Theorem of Calculus and the chain rule
$\displaystyle = .... $
You can do (b) in a similar way (the result is a chi-squared distribution with 1 df).
For (c), read 7.2 here: http://www.dartmouth.edu/~chance/tea...k/Chapter7.pdf