# Determining joint probability density function

1. Apr 8, 2012

### L.Richter

1. The problem statement, all variables and given/known data
A process X(t) is defined as

X(t) = Asin(ωt + $\phi$)

where A and $\phi$ are random variables while ω is a deterministic parameter. Note that A is a positive random variable.

Determine the joint probability density function, PDF, of X(t) and X'(t) in terms of the joint PDF of A and $\phi$.

2. Relevant equations
PDF of X(t), PX(t)(x) = ∫FX(x)dx

Is there another way to determine the PDF of a function that is multivariate, but not necessarily exponential, Gaussian or Gamma?

3. The attempt at a solution

I am not understanding how to get a joint PDF in terms of another joint PDF. Please advise. I'm not sure which functions belong where in the equations. I put the PDF equation since its the one I'm struggling with. I know that if I assume independence then I can get the joint PDF as a product of the individual PDFs. Thanks in advance!!

Last edited: Apr 8, 2012