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PDF of breaking a stick

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider a stick with unit length. We break at a point, the distance from which to the left end is a random variable X.

    Find the PDF of Z=|X-y|, where y is a set point between [0,1] (hint: define an event A and write fZ(z) = P(A)fZ|A(z) + P(Ac)fZ|Ac(z)).

    3. The attempt at a solution

    So basically, I set A to be the event {X<y}, so
    P(A) = ∫1dx from 0 to y = y.
    P(Ac) = ∫1dx from y to 1 = 1-y.

    Now, I need to find fZ|A(z) and fZ|Ac(z)
    I think my fundamentals are bad. Can someone please explain to me in words what the PDF is? Is it the probability of getting getting a value in a range of values? What exactly does the PDF mean in this problem?
    Can someone try and talk to me through finding fZ|A(z)?
    Thank you.
     
  2. jcsd
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