MATH 311 STATISTICS 1

Course Syllabus

1. INTRODUCTORY PROBABILITY

  1. Probability Spaces
  2. Finite Sample Spaces, Permutations and Combinations
  3. Partitions and Multinomial Coefficients
  4. Union of Events and Matchings
  5. Independence and Statistical Swindles

 

2. CONDITIONAL PROBABILITY

  1. Definition of Conditional Probability
  2. Bayes Theorem

 

3. RANDOM VARIABLES AND THEIR DISTRIBUTIONS

  1. Random Variables and Discrete Distributions
  2. Continuous Distributions
  3. The Distribution Function
  4. Bivariate Distributions
  5. Marginal Distributions
  6. Conditional Distributions
  7. Multivariate Distributions
  8. Functions of a Random Variable
  9. Functions of a Random Vector

 

4. EXPECTATION

  1. Definition of Expectation
  2. Properties of Expectation
  3. Variance
  4. Moments and the Moment Generating Function
  5. The Mean and the Median
  6. Covariance and Correlation
  7. Conditional Expectation

 

5. SPECIAL DISTRIBUTIONS

  1. The Chebyshev Inequality and the Law of Large Numbers
  2. The Bernoulli and Binomial Distributions
  3. The Hypergeometric Distribution
  4. The Poisson Distribution
  5. The Negative Binomial or Pascal Distribution
  6. The Gaussian or Normal Distribution
  7. The Central Limit Theorem and the Correction for Continuity
  8. The Gamma Distribution
  9. The Beta Distribution
  10. The Multinomial Distribution
  11. The Bivariate Normal Distribution

 

Prerequisites: MATH 141Students cannot receive credit for both MATH 311 and MATH 110.

 

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