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| − | =Lecture | + | =Lecture 38 Blog, [[ECE302]] Spring 2013, [[user:mboutin|Prof. Boutin]]= |
Friday April 12, 2013 (Week 14) - See [[LectureScheduleECE302Spring13_Boutin|Course Outline]]. | Friday April 12, 2013 (Week 14) - See [[LectureScheduleECE302Spring13_Boutin|Course Outline]]. | ||
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| − | In Lecture 38, | + | In Lecture 38, we started talking about the Poisson process. After giving a simple, somewhat incomplete definition, we obtained a simple expression for the mean of a poisson process. We then began studying how one could see the Process as a continuous analogue of the binomial counting process. Our first step towards that goal was to obtain an expression for the limit of the pmf of the binomial counting, as the number of steps becomes very large and the probability p of an event occurring becomes very small (while keeping the product np "moderate"). Remarkably, the limit pdf turned out to be that of a Poisson random variable. We will build on this result in the next lecture to fully understand the relationship between the Poisson random process and the binomial counting process. |
Latest revision as of 05:31, 15 April 2013
Lecture 38 Blog, ECE302 Spring 2013, Prof. Boutin
Friday April 12, 2013 (Week 14) - See Course Outline.
(Other blogs 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 32) 33) 34) 35) 36) 37)
In Lecture 38, we started talking about the Poisson process. After giving a simple, somewhat incomplete definition, we obtained a simple expression for the mean of a poisson process. We then began studying how one could see the Process as a continuous analogue of the binomial counting process. Our first step towards that goal was to obtain an expression for the limit of the pmf of the binomial counting, as the number of steps becomes very large and the probability p of an event occurring becomes very small (while keeping the product np "moderate"). Remarkably, the limit pdf turned out to be that of a Poisson random variable. We will build on this result in the next lecture to fully understand the relationship between the Poisson random process and the binomial counting process.
Action items for students (to be completed before next lecture)
- Solve problems 9.24 a)b) and 9.26 in the textbook. (You will hand in your solution as part of homework 7.)
Previous: Lecture 37
Next: Lecture 39
