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

# Lecture 10

1. New ideas in Chapter 4, p141
1. The random variable may now be continuous.
2. cumulative distribution function FX cdf
3. probability density function fX pdf
2. Example 4.1 review
1. cdf of # heads in 3 coin tosses
2. uses u(x)=1 if x>=0, 0 otherwise
3. what about cdf of 4 tosses?
4. ... # tosses to first head?
3. Example 4.2 review: cdf of uniform random variable over interval.
4. Example 4.3: uniform r.v. with a little extra
1. review total probability theorem
2. this r.v. is a mix of continuous and discrete
5. Example 4.4 shows finding probabilities when the cdf has jumps.
6. 4.1.1 3 types of r.v.: discrete, continuous, mixed.
7. 4.2 Probability density function (pdf) p148: derivative of cdf if that exists.
8. Example 4.6: uniform r.v.
9. Example 4.7: exponential r.v.
10. Example 4.8: laplacian r.v.
11. 4.2.1 pdf of discrete r.v.
1. unit step function
2. delta function: informally, a spike with 0 width, infinite height, and unit area.
12. Example 4.9: pdf of 3 coin toss
13. 4.2.2 conditional cdf and pdf
14. Example 4.10 conditional lifetime given still alive at t.
15. 4.3 Expected value p155
1. If r.v. is symmetric about x=m, then mean is m.
16. Example 4.12 uniform
17. Example 4.13 gaussian
18. Example 4.14 exponential
19. 4.3.1 Expected value of g(X)