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Math Help - Conditional density function

  1. #1
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    Conditional density function

    A number x is an element [0, infinity] is selected so as to have an exponential distribution with parameter alpha >0, that is fx(X) = alpha* e^-alpha*x for all x>=0 and zero otherwise. Once X = x is chosen, a second number Y is select so that it is uniformly distributed on the interval [ x, x+ beta] for soe constant B > 0.

    Calculate the conditional density function of f[y|x=x](y)?
    Ok so i knwo the formula for this is fx,y(x,y)/fy(y) but i have no idea where to get the y part....

    The answer is given by 1/beta....
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'd bet that you really want to find X|Y
    since it looks like we know that Y|X is uniform (X,X+B)
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  3. #3
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    Hi,thanks for replying!

    No its definitely Y|x=x
    The way i see to do it...after looking at a few examples is X+B - X = B
    and then put 1 over this....seems to work for the majority of the examples i have.....
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  4. #4
    MHF Contributor matheagle's Avatar
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    THIS READ AS a conditional...

    Once X = x is chosen, a second number Y is select so that it is uniformly distributed on the interval [ x, x+ B] for some constant B > 0

    This should be f_{Y|X}(y|X=x)={1\over B} when x\le y\le  x+ B.
    Last edited by matheagle; August 18th 2010 at 07:26 AM.
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