Solved: A stick of length 1 is broken at a uniformly random point, Basic Statistics

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A stick of length 1 is broken at a uniformly random point

Question: A stick of length 1 is broken at a uniformly random point, yielding two pieces. Let X and Y be the lengths of the shorter and longer pieces, respectively, and let R = X/Y be the ratio of the lengths X and Y.

(a) Find the CDF and PDF of R.

(b) Find the expected value of R (if it exists).

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Basic Statistics: A stick of length 1 is broken at a uniformly random point

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Basic Statistics: A stick of length 1 is broken at a uniformly random point

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