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Finding the conditional pdf

  1. Oct 27, 2010 #1
    Hi,

    This is a homework problem that I'm having a very hard time with. We are given that f(x)=e^(-x) for X greater/equal to zero. The question is to find f(x|A) where A is the union of the events (1 less/equal x, and x greater than 10). I can't figure out how to go about doing this....I thought of taking the complement of A and solving the conditional probability for x between 1 and 10, but then if I take 1 minus that, I don't think that f(x|A) will have an area less than 1, and it will also be negative at points. Any help is greatly appreciated.

    Thank you.
     
  2. jcsd
  3. Oct 27, 2010 #2

    mathman

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    f(x|A)=f(x)/∫Af(u)du, for xεA
    f(x|A)=0, otherwise
     
    Last edited: Oct 27, 2010
  4. Oct 27, 2010 #3
    Thanks for your help! But in this case, since A is less than 1 and greater than 10, what would the limits of the integral e? Also, what is f(u) in this case?
     
  5. Oct 28, 2010 #4

    mathman

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    The integral just gets split up into two parts (0,1) and (10,inf).

    Your second question makes me wonder about what level of math you are at. f is the function you are given. For the purpose of expressing the integral, u is just the dummy variable for integration - any other letter would do. I deliberately did not use x, since x is being used as the explicit variable for the expression.
     
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