ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute

# Lecture 14

- Tuesday's Maple worksheet is here: mar23.mws.
- Probability generating function for nonnegative r.v.
- Demo on Poisson.

- Exercise 4.69 on page 222. The random variable is S, the time for 7 passengers to arrive. It's 7-Erlang. See page 172. The number of passengers arriving in 10 minutes is N a Poisson r.v. with a=10. We want p(N<7), which is the probability that the van waits over 10 minutes.
- Exercise 4.102 on page 224. Characteristic function of U[-b,b]. See page 185. Use that to find mean.
- Chapter 5: Two r.v.
- Example 5.1 (height, weight). Possible event B: H<70, W<200.
- Example 5.3: Breaking a message into packets. Pair of r.v: (Q,R). Possible event: last packet < 1/2 full.
- pairs of discrete r.v.: joint pmf, marginal pmf.