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Math Help - 2 more questions

  1. #1
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    2 more questions

    1) Ley Y be a continuous random variable pdf f(y) = 1 - abs(y) for abs(y) less than or equal to 1. Set X = Y^2. Give the range of X. Derive the cdf and pdf of X.

    2) Let X be a continuous random variable with pdf f(x) = x/2 when 0 < x < 2. Let Y = 1/X. Find the pdf of Y.

    They are similar problems probably requiring the same method, but I don't understand what I'm supposed to do.
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  2. #2
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    Quote Originally Posted by Janu42 View Post
    1) Ley Y be a continuous random variable pdf f(y) = 1 - abs(y) for abs(y) less than or equal to 1. Set X = Y^2. Give the range of X. Derive the cdf and pdf of X.

    [snip]
    There are a variety of approaches. Here is one:

    cdf = F(x) = 0 for x < 0.


    cdf = F(x) = \Pr(X < x) = \Pr(Y^2 < x) = \Pr(-\sqrt{x} < Y < + \sqrt{x}) = \int_{-\sqrt{x}}^{+\sqrt{x}} 1 - |y| \, dy

    = \int_{-\sqrt{x}}^0 1 + y \, dy + \int^{+\sqrt{x}}_0 1 - y \, dy for 0 \leq x \leq 1 .


    cdf = F(x) = 1 for x > 1.

    Note that the pdf is found from dF/dx.


    Your other question can be done in a similar way.

    If you need more help please post all your working and say where yuo get stuck.
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