# HW8 - IE 111 Fall 2007 Homework #8 Due Friday November 2...

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IE 111 Fall 2007 Homework #8 Due Friday November 2 Question 1. Consider the following probability density function (PDF): f X (x) = kx 2 for 0 x 1 f X (x) = 0 otherwise a) Find k so that we have a valid probability density function. b) Find P(X 1). c) Find E(X). d) Find b so that P(X b) = 0.9. Question 2. Consider the following probability density function (PDF): f X (x) = kx for 0 x 1 f X (x) = k for 1 x 2 f X (x) = 0 otherwise a) Find k so that we have a valid probability density function. b) Find P(X 1). c) Find E(X). d) Find P(X>1.5). Question 3. Visitors arrive to a web site according to a Poisson process. On average we get one arrival every 15 seconds. a) What is the probability that we receive 16 or more visits in a 5 minute time period? b) Starting at 12 noon, what is the probability that the first visitor arrives after 12:01? c) Starting at 12 noon, what is the probability that the 25 th visitor arrives after 12:05? Question 4. On Tuesdays, patients arrive to the hospital at a rate of 2.5 per hour according to a Poisson process. I work an 8 hour shift at the hospital. a) Find the probability that exactly 20 patients arrive during my shift. b) Find the probability that 20 or fewer patients arrive during my shift.

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c) Find the probability that 10 or more patients arrive during my shift. d) On Mondays the patient arrival rate is 1.5 patients per hour (rather than 2.5 as on Tuesdays). Let X be the total number of patients that arrive during my shift on Monday and Tuesday. Find the expected value of X. Question 5. Dust particles land on my newly painted wall at a rate of 2.5 per hour. The wall is 8 feet by 12 feet. As long as the paint is wet, the dust particles will stick. It takes 8 hours for the paint to dry. a) Find the probability that exactly 20 particles stick to my wall. b) Find the probability that 20 or fewer particles stick to my wall. c) Find the probability that 10 or more particles stick to my wall. d) I decided to paint another wall which is 8 feet by 6 feet. Let X be the total number of dust particles that stick (over both walls). Find E(X). State any necessary assumptions. Question 6.
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## This homework help was uploaded on 02/26/2008 for the course IE 111 taught by Professor Storer during the Spring '07 term at Lehigh University .

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HW8 - IE 111 Fall 2007 Homework #8 Due Friday November 2...

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