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Consider a stick of length l . We break it randomly into two pieces and keep...

Consider a stick of length l . We break it randomly into two pieces and keep the piece, of length X, that contains the left end of the stick. We then repeat the same process on the piece we keep, and let Y be the length of the remaining piece after breaking the second time.

(a) Find the joint p.d.f of X and Y .

(b) Find Var(Y |X).

(c) Suppose that we break the stick at random point into two pieces and then break the piece that contains the right end of the stick, at random point. What is the probability that the three pieces we are left with can form a triangle?

Math   Statistics-And-Probability   
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