ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute
Lecture 10
- New ideas in Chapter 4, p141
- The random variable may now be continuous.
- cumulative distribution function FX cdf
- probability density function fX pdf
- Example 4.1 review
- cdf of # heads in 3 coin tosses
- uses u(x)=1 if x>=0, 0 otherwise
- what about cdf of 4 tosses?
- ... # tosses to first head?
- Example 4.2 review: cdf of uniform random variable over interval.
- Example 4.3: uniform r.v. with a little extra
- review total probability theorem
- this r.v. is a mix of continuous and discrete
- Example 4.4 shows finding probabilities when the cdf has jumps.
- 4.1.1 3 types of r.v.: discrete, continuous, mixed.
- 4.2 Probability density function (pdf) p148: derivative of cdf if that exists.
- Example 4.6: uniform r.v.
- Example 4.7: exponential r.v.
- Example 4.8: laplacian r.v.
- 4.2.1 pdf of discrete r.v.
- unit step function
- delta function: informally, a spike with 0 width, infinite height, and unit area.
- Example 4.9: pdf of 3 coin toss
- 4.2.2 conditional cdf and pdf
- Example 4.10 conditional lifetime given still alive at t.
- 4.3 Expected value p155
- If r.v. is symmetric about x=m, then mean is m.
- Example 4.12 uniform
- Example 4.13 gaussian
- Example 4.14 exponential
- 4.3.1 Expected value of g(X)