ECSE-2500 Engineering Probability, RPI, Spring 2011 Home Page

Homework 6, due 2pm Tues Mar 29, 2011

Notes

1. Email your solutions, as a PDF file, to

wrfranklin+homeworkATgmail.com , replacing AT with @.

1. You may do this homework in teams of two people.
2. Put the homework number, your names and RCS-IDs on the homework. (E.g. I would say something like Homework 3, W. Randolph Franklin, frankwr.)
3. Please put HW06 in your subject line.
4. This homework will be graded by Harish.
5. Many of these questions will require Matlab (or some other similar package).

Questions

1. (4 pts) Let X be a normal random variable with mean=10 and stdev=3 What is the probability that
   1. X<=5?
   2. 5<X<=10?
   3. 10<X<=15?
   4. 15<X?
2. (4 pts) Let X be a Poisson random variable with mean=10. What is the probability that
   1. X<=5?
   2. 5<X<=10?
   3. 10<X<=15?
   4. 15<X?
3. (4 pts) Let X be an exponential random variable with mean=10. What is the probability that
   1. X<=5?
   2. 5<X<=10?
   3. 10<X<=15?
   4. 15<X?
4. (10) Do exercise 4.73 on page 222 of the text.
5. (10) This exercise shows how the sum of independent r.v. start looking like a normal distribution.
   1. Compute the pdf of the sum of 2,3,4, and 5 independent r.v. that are each U[0,1].
   2. Compute the mean and standard deviation of each pdf.
   3. For each sum, plot the pdf and overlay it with a plot of the pdf of the normal distribution with the same mean and standard deviation.