# [SOLVED] find the cdf and pdf

• Dec 4th 2008, 09:48 AM
maths_123
[SOLVED] find the cdf and pdf
• Dec 6th 2008, 02:38 AM
mr fantastic
Quote:

Originally Posted by maths_123
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.
$F(t) = \Pr(T < t) = \Pr\left(\tan^{-1} \left( \frac{Y}{X}\right) < t \right) = \Pr\left(\frac{Y}{X} < \tan t \right) = \Pr(Y < (\tan t) X)$
$= \int_{x = 0}^{x = 1} \int_{y = 0}^{y = (\tan t) x} 2 \, dy \, dx = \, ....$
Then the pdf of T is given by $f(t) = \frac{dF}{dt} = \, ....$