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Finding probability given joint pdf.

  1. Nov 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Let X1 X2 X3 be independent and identically distributed random variables with common pdf f(x) = e^-x 0<x<infinity, zero elsewhere.

    Evaluate P(X1 < X2|X1 < 2X2) and P(X1 < X2 < X3|X3 < 1).


    3. The attempt at a solution

    Would appreciate any hints as to where to start...
     
  2. jcsd
  3. Nov 25, 2009 #2
    I haven't actually studied any statistics so there might be an easier way of doing this but this is how I'd do it...

    Having a conditional probability means that you essentially have a 100% probability for the condition, that is

    [tex] \int_{x_1 < 2x_2} dx_1 dx_2 f(x_1, x_2) = 1 [/tex]

    This gives you the probability density given the condition that x_1 < 2 x_2. You can then use that to find the probability that x_1 < x_2.
     
  4. Nov 25, 2009 #3
    But I don't think the problem is saying X1 < 2X2 I think the phrasing was X2|X1 < 2X2. Am I thinking about it wrong?
     
  5. Nov 26, 2009 #4
    The first problem reads out as "probability that x_1 < x_2, given that you already know that x_1 < 2x_2". The 2nd problem is "probability that x_1 < x_2 < x_3, given that you know that x_3 < 1". Atleast that is what this notation means as far as I know. :-)
     
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