- #1

ay0034

- 11

- 0

While doing a research, I obtained the following PDF:

[itex]f_{Z}[/itex][itex](z)=\frac{1}{2\pi\sigma^{2}_{1}\sigma^{2}_{2}}[/itex][itex]e^{-\frac{1}{2} ( \frac{\mu^{2}_{1}}{\sigma^{2}_{1}} + \frac{\mu^{2}_{2}}{\sigma^{2}_{2}})}[/itex][itex]\int^{2\pi}_{0}ze^{-\frac{1}{2\sigma^{2}_{1}\sigma^{2}_{2}}\{ \sigma^{2}_{2}z^{2}cos^{2}\theta+ \sigma^{2}_{1}z^{2}sin^{2}\theta-2\sigma^{2}_{2}\mu_{1}zcos\theta-2\sigma^{2}_{1}\mu_{2}zsin\theta \} }[/itex]

This integral won't be in a closed form. In addition to that, I have to integrate this PDF to get a CDF. Since this PDF is what I calculated, I want to check the CDF is going to be 1 as z goes to infinity.

However, both MATLAB and mathematica cannot integrate this PDF. Please help me with this annoying integration.

I appreciated it in advance.