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Homework Help: Determining joint probability density function

  1. Apr 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A process X(t) is defined as

    X(t) = Asin(ωt + [itex]\phi[/itex])

    where A and [itex]\phi[/itex] 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 [itex]\phi[/itex].


    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
  2. jcsd
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