Question

Suppose that the Route 29 northbound bus is scheduled to arrive at the 32nd Street and State Street stop on the hour, at 15 minutes past the hour, at 30 minutes past the hour, and at 45 minutes past the hour. However, due to random fluctuations, it arrives anywhere between 1 minute early and 2 minutes late with uniform distribution. Assume that the arrivals of different buses are independent and identically distributed (IID). Compute by hand the following probabilities:________.

a) The probability of four successive buses all not being late;

b) The probability of needing to wait for more than 15 minutes for a bus if you arrive at the stop at noon; and

c) The expected time required to wait for a bus if you arrive at the bus stop at a random time is 7.55. Create a Monte Carlo simulation to compute the expected time. What answer do you compute using 106 runs?

Answer 1

Answer:Suppose that the Route 29 northbound bus is scheduled to arrive at the 32nd Street and State Street stop on the hour, at 15 minutes past the hour, at 30 minutes past the hour, and at 45 minutes past the hour. However, due to random fluctuations, it arrives anywhere between 1 minute early and 2 minutes late with uniform distribution. Assume that the arrivals of different buses are independent and identically distributed (IID). Compute by hand the following probabilities:________.

a) The probability of four successive buses all not being late;

b) The probability of needing to wait for more than 15 minutes for a bus if you arrive at the stop at noon; and

c) The expected time required to wait for a bus if you arrive at the bus stop at a random time is 7.55. Create a Monte Carlo simulation to compute the expected time. What answer do you compute using 106 runs?Suppose that the Route 29 northbound bus is scheduled to arrive at the 32nd Street and State Street stop on the hour, at 15 minutes past the hour, at 30 minutes past the hour, and at 45 minutes past the

Explanation: