1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statistics - joint and marginal densities.

  1. May 27, 2013 #1
    Hi,
    1. The problem statement, all variables and given/known data
    I am having difficulties understand parts of the solution to the following problem in Statistics:
    Let X and Y be two random, continuous variables, where X is distributed U(0,1) and Y|X=x is distributed U(x,x+1). I am asked to find the marginal density of Y.

    2. Relevant equations



    3. The attempt at a solution
    For that I would first need to find the joint density. I know that the double integral of the joint density over the area defined by the lines y=x, y=x+1, x=1, x=0 (parallelogram) is 1. What I don't quite comprehend is why would the joint density then be 1/A where A is the area of the parallelogram in this case.
    Next, suppose fX,Y(x,y) = 1, why do I need to separate fY(y) = ∫ (between -inf. and +inf.) dx into two integrals (one for 0 ≤ y ≤ 1 and one for 1 ≤ y ≤ 2)? Why couldn't I use one integral? And why are the integration boundaries for the second integral y-1 and 1? How could I have figured it out?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Statistics - joint and marginal densities.
Loading...