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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.