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

# Lecture 13

1. The Maple worksheet from last time is here: Gfiles:mar19.mws.
2. Maple cheat sheet:
1. ?Statistics
2. with(Statistics);
3. X:=RandomVariable(Uniform(0,1));
4. x:=PDF(X,t);
5. Mean(X), Variance(X), StandardDeviation(X);
6. plot(x,t=-2 ... 3);
7. plot(PDF(X^2,t),t);
3. iclicker exercise: One random variable has the memoryless property. Which is it?
• A: beta
• B: cauchy
• C: exponential
• D: normal
• E: uniform
4. Most other probability distributions converge to which of the probability distributions when you add many independent random variables?
• A: beta
• B: cauchy
• C: exponential
• D: normal
• E: uniform
5. Which of the following has no moments?
• A: beta
• B: cauchy
• C: exponential
• D: normal
• E: uniform
6. Example 4.22, p169. - in several stages.
7. Gamma r.v.
8. Example 4.24, computation in Maple, comparison to book.
9. Derivation of Markov inequality
10. Characteristic function, with geometric distribution as example.