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 Xn be the length of the piece that remains after the stick has been broken n times. Describe Xn as a product.

(b) Prove that

639_Prove that.png

and determine the limit.

(c) Find the distribution of the length of the first piece that was thrown away - don't compute, think! Then compute.

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