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Math Help - Probability question- how do I find the CDF?

  1. #1
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    Jerusalem
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    Probability question- how do I find the CDF?

    The question: Given that a random variable X is uniformly distributed on (-1,1) and Y=max(X, 1-X), find the CDF of Y.

    I tried to solve as following:
    First I found the CDF of X, then I tried to find the relation between the CDF of X and the CDF of Y.
    Y=max(X, 1-X) means that for x<0.5 y=1-x, and for x>0.5 y=x
    So FY(alpha)=P(Y<alpha) but here I have a problem: which Y should I use? (y=x or y=1-x or both in some complicated way)

    I've been thinking this over and over, but I just CAN'T find the solution.
    Can you please please help me?
    Thanks!
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  2. #2
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    Mar 2012
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    kanpur, india
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    Re: Probability question- how do I find the CDF?

    try this.. P(Y<=y)=P(max(X,1-X)<=y) = P(X<=y,1-X<=y)=P(1-y<=X<=y)
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  3. #3
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    Re: Probability question- how do I find the CDF?

    Thanks, I'll try.
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