Question

1) We have a stick of unit length. We break that into 3 pieces using the following methods

a. We chose randomly and independently two points on the stick using a uniform PDF, and we break stick at these 2 points

b. 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

c. We break the stick at a random point chosen by using a uniform PDF, and then we break the larger of the 2 pieces at a random point chosen by using a uniform PDF.

For each of the methods a, b, c, what is the probability that the three pieces we are left with can form a triangle

Answer 1