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Independent random variables max and min

  1. Apr 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Let X and Y be two independent random variables with distribution functions F and G, respectively. Find the distribution functions of max(X,Y) and min(X,Y).


    2. Relevant equations



    3. The attempt at a solution
    Can someone give me a jumping off point for this problem? All I can think of is that the distribution function for max(X,Y) is F for X>Y and G for Y>X. That seems a little too simple though.
     
  2. jcsd
  3. Apr 7, 2009 #2
    Let H(t) be the distribution function of max(X,Y). What does the definition of distribution function say that H(t) is equal to?
     
  4. Apr 7, 2009 #3
    I am really struggling with the material since the midterm, so I am not sure I know what you are asking. Are you referring to H(t) = P(X [tex]\leq[/tex] t) ?
     
  5. Apr 7, 2009 #4
    Exactly! Only in this case it is max(X,Y) instead of X.

    Now, think about it means for max(X,Y) to be [tex]\leq[/tex] t. What must be true about X and/or Y?
     
  6. Apr 7, 2009 #5
    it means that
    P(max(X,Y) [tex]\leq[/tex] t) =
    P(X [tex]\leq[/tex] t)P(Y [tex]\leq[/tex] t) =
    F*G

    yes, no, maybe?

    this part for min(x,y) i am pretty sure was wrong, so looking into it more.
     
    Last edited: Apr 7, 2009
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