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Finding probability of a minimum

  1. Nov 26, 2011 #1
    let X1 and X2 be two randomly selected random variables from the same discrete distribution. Let Y=min(X1,X2). Find P(Y=1)

    according to the book. P(Y=1)=P[(X1=1)and(X2>=1)]+P[(X2=1)and(X1>=2)]

    I don't understand why is the asymmetry is even possible. The way I look at it, it's
    P(Y=1)=P[(X1=1)and(X2>1)]+P[(X2=1)and(X1>1)]
     
  2. jcsd
  3. Nov 26, 2011 #2

    Stephen Tashi

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    In the case of discrete random variables, your way omits the event "X1 = 1 and X2 = 1". In the case of continuous random variables (where that event has zero probability), your method is correct.

    The book's way is correct for the case of discrete random variables that only take integer values. It wouldn't be correct for continuous random variables.
     
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