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Thread: Finding pdf question

  1. #1
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    Last edited by JaguarXJS; Dec 15th 2016 at 07:59 PM.
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  2. #2
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    Re: Finding pdf question

    you can note that

    $P[\cos(X) < y] = 2 P[X < \cos^{-1}(y)]$

    When you look at this carefully you find that

    $2 P[X < \cos^{-1}(y)] = 1- \dfrac 1 \pi \cos^{-1}(y)$

    with a resulting PDF of

    $\dfrac{1}{\pi \sqrt{1-y^2}},~-1 \leq y \leq 1$
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