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Math Help - Normal random variable question

  1. #1
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    Normal random variable question

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

    Thanks
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  2. #2
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    Quote Originally Posted by neild View Post
    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
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