A stick of length L is broken at a random point uniformly distributed on the interval [0, L]. Two new sticks are formed. a) If X denotes the length of the longest new stick, calculate E(X) and V(X)
b) If Y denotes the length of the shortest new stick, calculate E(Y) and V(Y) Hint: X+Y = L, and L is not a random number.
c) An experiment consists on breaking sticks of length L independently as described before until the longest new stick has length of at least 0.9L. What is the expected number of sticks to be broken in this experiment.