A delivery truck operates from a warehouse to a department store, and its trip duration is a random variable D in minutes. Once it reaches the department store, it takes time T to unload. To simplify the problem, the random variables D and T are assumed to take on discrete values with associated probabilities as follows:

(a) Define the sample space of all the possible scenarios of D and T.

(b) Construct a probability tree.

(c) Assuming events defining D and T are independent, compute the probability mass function of the total time to deliver and unload.

(d) Assuming that the truck makes a return trip to the warehouse with the return trip duration having the same probability mass function as the delivery duration although independent of it, compute the total duration of a complete cycle of delivery, unload and return.

(e) Compute the probability that the duration of a complete cycle will be less than 1 h.

Transcribed Image Text:

D (min) P(d) T (min) P,(t) 10 0.1 5 0.3 20 0.3 10 0.25 30 0.5 15 0.35 40 0.1 20 0.1