1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook