Students with documented disabilities: If you are seeking classroom accommodations under the Americans with Disabilities Act, you are required to register with the Center for Academic Achievement, located in Duffy 109. To receive academic accommodations for this class, please request an accommodation letter from the Center for Academic Achievement and meet with me at the beginning of the semester.

MA395-A Fall 2006 Syllabus

WeekDatesText
Section		Topic(s)
1 8/29 8/31 1.1History and Examples
1.2
  • Set Theory
    • Venn diagrams
    • cardinality
    • algebras of sets
    • set functions
  • Basic definitions
    • experiment
    • outcome
    • event
    • sample space
2 9/5 9/7 2.3The Kolmogorov Axioms
2.4Conditional probability; Bayes theorem
2.5Independence
3 9/12 9/14 2.6Combinatorics
  • multiplication rule
  • permutations
  • combinations
2.7combinatorial probability
2.8monte carlo methods
4 9/19 9/21 3.1definition of a discrete random variable
3.2binomial and hypergeometric distributions
3.3discrete probability distributions
  • the probability function
  • the probability density function
  • the cumulative distribution function
  • linear transformations of a discrete random variable
5 9/26 9/28 3.4continuous probability distributions
  • the probability function
  • the probability density function
  • the cumulative distribution function
  • linear transformations of a continuous random variable
6 10/3 10/5 3.5
  • expected values
    • the discrete case
    • the continuous case
  • measures of central tendency
    • the mean
    • the median
  • expected value of a function of a random variable
3.6the variance and higher moments
7 10/10
No
Classes		 10/12 3.7joint densities
  • discrete joint densities
  • continuous joint densities
  • the marginal PDF
  • the joint CDF
8 10/17 10/19 3.7
  • multivariate densities
  • independence
  • random samples
3.8
  • combining random variables
    • PDFs of sums
    • PDFs of products and quotients
  • the mean and variance of a multivariate distribution
  • the variance of a sum
9 10/24 10/26 3.11conditional densities
  • discrete
  • continuous
3.12moment generating functions
  • finding momemts with MGFs
  • identifying PDFs using MGFs
10 10/31 11/2 4.2the Poisson and exponential distributions
  • the law of small numbers
4.3the normal distribution
  • the DeMoivre-Laplace limit theorem
  • the central limit theorem
11 11/7 11/9 5.1introduction to estimation
5.2
  • maximum likelihood estimation
  • method of moments estimation
5.3
  • interval estimation
  • confidence intervals
  • sample size
  • margin of error
12 11/14 11/16 5.4properties of estimates
  • unbiased
  • efficient
5.5 the Cramer-Rao lower bound
  • minimum variance estimation
  • efficiency
5.6 sufficiency
13 11/17 11/19
No
Classes		 5.7consistency
  • convergence in probability
  • Chebyshev's law
14 11/28 11/30 6.2hypothesis testing
  • decision rules
  • one-sided versus two-sided alternatives
  • level of significance
  • P-values
15 12/5 12/7 6.4
  • type I errors
  • type II errors
  • the power of a test
6.5generalized likelihood ratios
FINAL EXAM THURSDAY, DEC 14 8:30 AM C-209