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Monday June 27, 2005

The final grade is out. I hope that this has been a useful course. I wish all success in future courses.

new Posted @ 2:02 PM

Thursday May 26, 2005

Don't forget [HSU 2000]. It has good material on the Poisson process. It can also help with concrete (numerical) exercises to check your understanding of concepts and relations. Sometimes it may also contain straight answers!

Posted @ 7:24 AM

I've updated the report guidelines and criteria. Please re-read carefully before you submit project 3.

Posted @ 7:15 AM

On TMR-2standby system, the system is clearly 2 sequential phases of: ~exp(3lambda) and 2-stage Erlang(lambda). The MGF of the system is simply the product of the MGFs of phases. From the table on page 778, you can pick up the MGF of the exponential (with 3lambda substituted for lambda) and the MGF of the Erlang (with r=2). Differentiate the product (an algebraic expression) either manually (use the product rule (fg)'=fg'+f'g), or use Maple. Amazing this Laplace thing.

Another important note about math logic. You can't make a general statement based on one case. Only one of you got it right.

Posted @ 6:55 AM

Monday May 23, 2005

It's important to seed your random number generator differently for each sample path simulation in order to get a different path each time.

Posted @ 10:00 PM

Use this C code as reference for generating exponentially-distributed sample.

Posted @ 9:20 PM

Tuesday, May 17, 2005

For Sunday I only need to check your simulation. Show me plots or tables of one or two sample paths. In particular, I need to check that your interarrival times are from an exponentially-distributed sample.

What your can do to demonstrate the quality of your sample is to use results from 4.7. Show me that your sample mean is close enough to the known mean of the exponential distribution.

For Sunday don't worry about presentation.

Posted @ 8:50 PM

I regret missing today's class. Sorry for any inconvenience. We will resume next Sunday

Posted @ 8:45 PM

Tuesday, May 10, 2005

Regarding today's problem. Like I commented, in this case we know that the passwords are equally likely. So what's the probability of getting a 6 when you roll a die? Exactly the same logic leads us to conclude that N_n = 1/n, that is, uniformly distributed.

This is the trivial case of the hypergeometric distribution when you have exactly one defective in the pool and you draw a sample of 1. In other words, h(1;1,1,n). Compute it yourself!

A similar situation arises when unsuccessful passwords are not eliminated (sampling with replacement). While you all correctly figured out that N_n is geometric, a binomial model would have worked just as well, only the model would have been needlessly complicated. After all, the geometric r.v. is just a special case of the binomial.

Posted @ 11:05 PM

Monday, April 25, 2005

Check this page if you're having trouble generating the required data for project 2.

Posted @ 11:05 PM

Saturday, April 16, 2005

You may have noticed that I've not been keeping up with your work as I should. I was swamped with admin work, particularly involving our upcoming College of Computing and IT. I've decided that my priorities should be straightened. I'm not wasting anymore time on that ...

I've always prided myself on being teaching-oriented. I will try my best to make it up for the rest of the semester.

meanwhile, you guys need to start arranging for the course exam. It may have to be pushed a week later though.

Posted @ 6:00 AM

Tuesday, March 15, 2005

Solution to [HSU 2000] problem 1.3. Try this hint before you check the answer: the trials before 6 are ordered with replacement, a structure which can be generated via a Cartesian product.

Posted @ 6:45 PM

Saturday, March 12, 2005

And, here is Maple set for studying binomial approximation.

Posted @ 10:55 PM

Please get the slides for lecture 4 as well. We'll refer to some of them tomorrow.

Posted @ 10:25 PM

Sunday, March 6, 2005

Please include in the subject of your homework emails the keyword 'homework' and the assignment session number. For example: Homework Session 8, or some such thing.

Posted @ 10:40 PM

This week would be a good time to read up on Kolmogorov, one of the most important mathematicians of our times.

Posted @ 8:58 PM

Here is maple worksheet set 1, including the long promised plot example.

Posted @ 8:25 PM

Tuesday, February 28, 2005

I've prepared a CD for each of you containing the stuff you'll need for this course. You should get it tomorrow.

We'll start this weekend to familiarize with Maple (get this worksheet set on counting). Sign-up for the free "Maple Essentials" tutorial (linked from my Maple help page).

I also want you to explore around the Virtual Probability Lab website. It can help you better learn and visualize the ideas covered so far.

Posted @ 8:35 PM

Sunday, February 20, 2005

We still don't have a room. I was promised that the situation will definitely be resolved by next Tuesday. I have already informed concerned parties. That's the best I'm willing to do. Sorry. Keep hoping and praying.

Meanwhile please get the textbooks and start reading Sections 1.1-1.8 in Trivedi.

Posted @ 1:50 PM

Friday, February 18, 2005

Again bad scheduling delays our class. As of last Tuesday we had no room. I was promised that room 209 will be available next time. We can only hope and pray.

Posted @ 10:00 PM

Sunday, February 13, 2005

Due to scheduling difficulties we were unable to start today as planned. The first lecture will be on Tuesday February 15. The rooms are 209 in building 75, and 923 on the ladies' side. I adjusted the calendar accordingly.

Meanwhile try to get the textbooks at Mars (al-Marreekh) Publishing.

Posted @ 6:55 PM

Friday, February 11, 2005

Check the revised syllabus which includes a tentative teaching schedule. The topics and slides for each lecture will appear the night before in the course calendar.

Posted @ 3:00 PM

Thursday, February 10, 2005

First lecture will be on Sunday February 13, 2005 (4/1/1426), insha Allah.

Posted @ 9:40 PM

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