A stick of length 1 is randomly broken which means that the, Basic Statistics

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A stick of length 1 is randomly broken which means that the

A stick of length 1 is randomly broken, which means that the remaining piece is U(0, 1)-distributed. The remaining piece is broken similarly, and so on.

(a) Let X_n be the length of the piece that remains after the stick has been broken n times. Describe X_n as a product.

(b) Prove that

and determine the limit.

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