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What does this mean? P(|Y - 1/2| > 1/4)? (2nd year stats)

  1. Feb 11, 2008 #1
    1. The problem statement, all variables and given/known data

    The question is

    Let Y be a continuous random variable with pdf f_Y(y) = 3(1-y)^2

    and I have to find P(|Y - 1/2| > 1/4)


    2. Relevant equations

    Is there a formula involved here or something that can help me???


    3. The attempt at a solution

    I'm not even sure how to find the probability of a pdf once it's given, is there a formula that I can use and plug the values in... I think it's more confusing that there is an inequality in the probability as well... any hints will be greatly appreciated
     
  2. jcsd
  3. Feb 11, 2008 #2

    chroot

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    Staff Emeritus
    Science Advisor
    Gold Member

    Well, break the absolute value into two parts first.

    If you're looking for the region where | Y - 1/2 | > 1/4, that's the same as looking for the combined areas where Y - 1/2 > 1/4 and where -( Y - 1/2 ) > 1/4.

    In other words, you need to find the total probability that Y > 3/4, added to the total probability that Y < 1/4. Both of these total probabilities can be found by integrating the pdf.

    - Warren
     
  4. Feb 11, 2008 #3
    Wow!! Thanks heaps warren that is great help!
     
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