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Finding cdf and pdf of variable.

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

    Let X1 X2 X3 and X4 be four independent random variables, each with pdf f(x) = 3(1-x)2, 0<x<1, zero elsewhere. If Y is the minimum of these four variables, find the cdf and pdf of Y.

    3. The attempt at a solution

    P(Y<or= y)

    = 1 - P(Y>y)
    = 1 - P(X1>y, X2>y, X3>y, X4>y)
    = 1 - P(X1>y)P(X2>y)P(X3>y)P(X4>y)
    = 1 - [3(1-x)2]4

    which does NOT equal (1-y)12, which is the answer in the back of the book. Don't know where I'm going wrong...
     
  2. jcsd
  3. Nov 25, 2009 #2
    What is P(x_1 > y)? It's certainly not that. Maybe you should try integrating over f instead.
     
  4. Nov 25, 2009 #3
    Got it! Thanks so much for the help.
     
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