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Ind rand variable distribution

  1. Apr 2, 2008 #1
    Hi Guys.

    I'm trying to understand how to solve the following problem. Any help and explanation would be greatly appreciated!

    Let X and Y be independent N(0, 1) random variables and let Z = X + Y.

    What is the distribution of Z? Write down the density function of Z.
    Show that E[Z|X > 0, Y > 0] = 2
  2. jcsd
  3. Apr 3, 2008 #2


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    Have you learned about characteristic functions(cf)? If so then you get the cf of Z is the product of the cf's of X and Y. The cf of Z is then exp(-t2), so that Z is normally distributed with a variance of 2.

    For the last question, set it up as a ratio of double integrals in x and y. Then convert to polar coordinates. It should be tedious, but workable.
  4. Apr 4, 2008 #3


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    If X~N(m1,s1^2) and Y~N(m2,s2^2) indeply, then
    X(+-)Y ~ N(m1(+-)m2,s1^2+s2^2), it is easier to check from mgf or cf.
  5. Apr 7, 2008 #4
    I'm still somewhat confused. What would you say as the final answer to the two questions I have above....?

    If you could just list something like:
    answer: thefunc
    reason: because x y and z

    Sorry if it seems bossy, I'm just really confused now after reading the above.
  6. Apr 7, 2008 #5

    It's hardly possible to state the answer to 1) more explicitly.
  7. Apr 9, 2008 #6


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    No, you have to add 'and mean=0'. LOL.
  8. Apr 9, 2008 #7
    O.k., you're right, of course.:smile:
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