Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conditional Probability, Additive Signals

  1. Apr 16, 2013 #1
    Obviously, this is a homework assignment, so I don't want it done for me; however, I am confused. Perhaps I am just confused by the problem or the wording, but I am totally stuck on what to do.

    I believe the output signal should be a convolution where Z = X + Y, and Y is the gaussian(0, 2). After I solve the convolution and receive Z, I don't know what to do.
  2. jcsd
  3. Apr 17, 2013 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    My guess is that you need to solve for the conditional cumulative distribution [itex] F(w,y) = P(X + Y \le w | Y = y) = P(X \le w - y | Y = y) [/itex]. Then differentiate with respect to w to get the density. (I think you interpreted "gaussian noise channel" correctly in the context of the problem, but I think it has an interpretation as a continuous stochastic process in other contexts.)
    Last edited: Apr 17, 2013
  4. Apr 17, 2013 #3

    Stephen Tashi

    User Avatar
    Science Advisor

    If g(X,Y) is joint density of the convolution X + Y, can you set Y = y and integrate symbolically with respect to X from minus infinity to w-y to obtain [itex] P(X \le w -y| Y = y) [/itex]? (I haven't worked the details out, so I don't know.)
  5. Apr 17, 2013 #4


    User Avatar

    If output (Z)= noise(Y) + signal (X) then the following is the working principle:
    Find the distribution of Z.
    Then from the joint distribution Z and X find the distribution X|Z.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook