Question

# 4. The honours project for Jacob, a computer science student at Carleton, is to develop a...

4. The honours project for Jacob, a computer science student at Carleton, is to develop a program that performs a certain task. Jacob noticed that his program will complete the task successfully. However the times of completion differ depending on the parameters he feeds his program. Assume that completion times follow an exponential distribution with mean 1.5 hours. What is the probability that Jacob's program takes

A. less than 45 minutes to complete a task?
B. between 1 and 2.5 hours to complete a task? C. more than 2 hours to complete a task?

P(X<= a)= 1- e^(-a/μ)

It is given that completion times in hours (say ) follow an exponential distribution with mean 1.5 hours.

Thus, .

The PDF and CDF are

A) The probability that Jacob's program takes less than 45 minutes to complete a task is

B. The probability that Jacob's program takes between 1 and 2.5 hours to complete a task is

C) The probability that Jacob's program takes more than 2 hours to complete a task is

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