# Math Help - Normal random variable question

1. ## Normal random variable question

I really do not understand this question. Could anyone point me in the right direction?

Thanks

2. Originally Posted by neild
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:

$\displaystyle G(y) = \Pr(Y \leq y) = \Pr(aX + b \leq y) = \Pr\left(X \leq \frac{y - b}{a}\right)$ (assuming a > 0)

$\displaystyle = \int_{-\infty}^{\frac{y - b}{a}} f(x) \, dx$ where f(x) is the pdf of x.

Therefore the pdf of Y is:

$\displaystyle g(y) = \frac{d G}{dy} = f\left( \frac{y - b}{a}\right) \cdot \frac{1}{a}$ using the Fundamental Theorem of Calculus and the chain rule

$= ....$

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