MCS 341 EXAM 2
  • When: Monday, October 18, 10:30-11:20
  • What: An examination consisting of problems related to Chapter 3, Discrete Random Variables and Their Probability Distributions (sections 3.1-3.9) and supplementary class notes.
  • Where: Our classroom, Olin 219
  • How: Closed-book, but with one new 3"-by-5" note card allowed. (You may also use your note card from the previous exam.)
    TOPICS
  • Random variables
    • Discrete random variables
  • The probability distribution for a discrete random variable
    • The probability function
    • Properties of a probability function (p. 86)
  • Expected values (means, expectations)
    • Definition of E(Y) if Y is discrete
    • Law of the Unconscious Statistician
    • Definition and formulas for the variance
    • Standard deviation
    • Properties of expected values
  • Properties of variance and covariance
    • Definition of covariance, correlation coefficient
    • Variance and covariance of sums of random variables
    • Independent random variables
    • E(XY) for independent X and Y
    • Variance of a sum of independent or uncorrelated random variables
  • Bernoulli trials (B-trials)
  • The binomial probability distribution
    • Standard model: the "binomial experiment," p. 97
    • Probability function
    • Mean and variance
    • Binomial theorem
  • The geometric probability distribution
    • Standard example: In B-trials, the number of the trial on which the first success occurs
    • Probability function
    • Mean and variance
    • Sum of a geometric series
  • The negative binomial distribution
    • Standard example: In B-trials, the number of the trial on which the rth success occurs
    • Probability function
    • Mean and variance
  • The hypergeometric probability distribution
    • Standard example: The number of "successes" in a random sample from a finite population
    • Probability function
    • Mean and variance
  • The Poisson probability distribution
    • Standard example: The number of "arrivals" in a given interval when the three assumptions stated in class are satisfied
    • Probability function
    • Mean and variance
    • Series for ex
  • Moments and moment-generating functions
    • The kth moment
    • The kth central moment
    • The kth factorial moment
    • The moment generating function E(etY)
    • Maclaurin series
    REVIEW QUESTIONS
  • Review problems: discrete random variables (ps)  (pdf)
  • Review problems: discrete random variables--answers (ps)  (pdf)