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

# Lecture 13

- The Maple worksheet from last time is here: Gfiles:mar19.mws.
- Maple cheat sheet:
- ?Statistics
- with(Statistics);
- X:=RandomVariable(Uniform(0,1));
- x:=PDF(X,t);
- Mean(X), Variance(X), StandardDeviation(X);
- plot(x,t=-2 ... 3);
- plot(PDF(X^2,t),t);

- iclicker exercise: One random variable has the
*memoryless*property. Which is it?- A: beta
- B: cauchy
- C: exponential
- D: normal
- E: uniform

- 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

- Which of the following has no moments?
- A: beta
- B: cauchy
- C: exponential
- D: normal
- E: uniform

- Example 4.22, p169. - in several stages.
- Gamma r.v.
- Example 4.24, computation in Maple, comparison to book.
- Derivation of Markov inequality
- Characteristic function, with geometric distribution as example.