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Math Help - [SOLVED] find the cdf and pdf

  1. #1
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    Exclamation [SOLVED] find the cdf and pdf

    Hi can someone please help me with this question
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  2. #2
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    Quote Originally Posted by maths_123 View Post
    Hi can someone please help me with this question
    The joint cdf of X and Y is f(x, y) = 2 for 0 \leq x \leq 1, \, 0 \leq y \leq 1 and zero otherwise.

    The cdf of T is given by:

    F(t) = \Pr(T < t) = \Pr\left(\tan^{-1} \left( \frac{Y}{X}\right) < t \right) = \Pr\left(\frac{Y}{X} < \tan t \right) = \Pr(Y < (\tan t) X)

    = \int_{x = 0}^{x = 1} \int_{y = 0}^{y = (\tan t) x} 2 \, dy \, dx = \, ....

    Then the pdf of T is given by f(t) = \frac{dF}{dt} = \, ....
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