Hi can someone please help me with this question

Printable View

- Dec 4th 2008, 08:48 AMmaths_123[SOLVED] find the cdf and pdf
Hi can someone please help me with this question

- Dec 6th 2008, 01:38 AMmr fantastic
The joint cdf of X and Y is $\displaystyle f(x, y) = 2$ for $\displaystyle 0 \leq x \leq 1, \, 0 \leq y \leq 1$ and zero otherwise.

The cdf of T is given by:

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

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

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