We have a stick of unit length, and we consider breaking it in three pieces usin

Question

We have a stick of unit length, and we consider breaking it in three pieces using one of the following three methods.

(i) We choose randomly and independently two points on the stick using a uniform PDF, and we break the stick at these two points (i) We break the stick at a random point chosen by using a uniform PDF, and then we break the piece that contains the right end of the stick, at a random point chosen by using a uniform PDF. (ii) We break the stick at a random point chosen by using a uniform PDF, and then we break the larger of the two pieces at a random point chosen by using a uniform PDF. For each of the methods(), (i), and (iii), what is the probability that the three pieces we are left with can form a triangle? Hint: If X, Y and 1 - X - Y are the lengths of the three pieces, respectively, then in order for them to form a triangle the following inequality needs to hold: , r an

Explanation / Answer

We have a stick of unit length, and we consider breaking it in three pieces usin

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