Question

CHAPTER 2-3

2.14

A construction job is comprised of two tasks, which we will call ''task A" and "task B." The two tasks are initiated simultaneously and their completion times are uncertain. The entire construction job is completed as soon as both tasks are completed. The possible outcomes for the completion times of task A and task B, and the associated probabilities, are given in Table 2.28.

TABLE 2.28 Probabilities of time to completion of tasks A and B. Time to Complete Task A (in weeks) Time to Complete Task B (in weeks) Probability 1 1 0.07 1 2 0.27 1 3 0.06 2 1 0.13 2 2 0.31 2 3 0.16

		(a) What is the probability distribution of the duration of task A? of task B? of the job as a whole?

		(b) What is the mean and the standard deviation of the duration of task A? of task B? of the job as a whole?

		(c) Suppose that task A costs $800 for every week that it is in progress, and that task B costs $1,000 per week for every week that it is in progress, and that there is an additional charge of $400 for every week that the job as a whole is still in progress. Compute the probability distribution, the mean, and the standard deviation of the cost of this construction job.

Exercise 2.19

A package delivery company experiences high variability in daily customer demand, which in turn results in high variability in the daily workload at the central sorting facility. The company relies on its sorting facility employees working overtime to provide on-time delivery when the workload demand is very high. A sorting facility employee receives a salary of $12/hour for a 40 hour week, and the employee receives $18/hour for every hour worked overtime, that is, for every hour worked over 40 hours in a given week. The number of overtime hours that an employee works in any given week is a random variable, with a mean of 15 hours and a standard deviation of 4 hours. What are the mean, the standard deviation, and the variance of an employee's total weekly salary?

Answer 1

Note:Due to little confussion about 2.14 in c bit so i couldn't solved.If you want to answer for that bit please post it separately.

Thank you.