Let X equal the arrival time of the third elevator in Quiz 7.2. Find the exact value of P[W ≥ 60]. Compare your answer to the upper bounds derived in Quiz 7.2.
Quiz 7.2
Elevators arrive randomly at the ground floor of an office building. Because of a large crowd, a person will wait for time W in order to board the third arriving elevator. Let X1 denote the time (in seconds) until the first elevator arrives and let X i denote the time between the arrival of elevator i - 1 and i. Suppose X1, X2, X3 are independent uniform (0, 30) random variables. Find upper bounds to the probability W exceeds 75 seconds using.
(1) the Markov inequality,
(2) the Chebyshev inequality.