(adsbygoogle = window.adsbygoogle || []).push({}); 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 f_{Z}(z) = P(A)f_{Z|A}(z) + P(A^{c})f_{Z|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(A^{c}) = ∫1dx from y to 1 = 1-y.

Now, I need to find f_{Z|A}(z) and f_{Z|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 f_{Z|A}(z)?

Thank you.

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# Homework Help: PDF of breaking a stick

Can you offer guidance or do you also need help?

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