MATH 340, Study Guide for Midterm Test 2

4/20/2014

Test coverage

4. Random Variables
   1. Random variables: examples (4.1)
   2. Discrete random variables: probability mass function, cumulative distribution function (4.2)
   3. Expectation of a random variable (4.3)
   4. Expectation of a function of a random variable (4.4)
   5. Variance (4.5)
   6. The Bernoulli and Binomial random variables (4.6)
   7. The Poisson random variable (4.7)
   8. Other discrete probability distributions: Geometric, Negative Binomial (4.8.1, 4.8.2)
   9. Properties of the Cumulative Distribution Function (4.9)
   10. Summary after the Chapter to be used for review
5. Continuous Random Variables
   1. Introduction: concept of probability density (5.1)
   2. Expectation and Variance (5.2)
   3. Uniform random variables (5.3)
   4. Normal random variables (5.4)
   5. The normal approximation of the binomial distribution; "0.5 correction" (5.4.1)
   6. Exponential random variables (5.5); skip 5.5.1 and 5.6
   7. Distribution of a function of a random variable (5.7: Example 7a, problem 5.40)
6. Jointly distributed random variables
   1. Joint distribution functions (6.1)
   2. Independent random variables (6.2)

Key concepts

• Discrete random variables, probability mass functions and CDFs
• Graphic representation of probability mass functions and CDFs
• Expectation, variance; expectation of a function of a random variable
• Basic types of discrete distributions: Bernoulli, Binomial, Poisson, Geometric, Negative Binomial
• Probability density, the cumulative distribution function
• Expectation, variance; expectation of a function of a random variable
• Continuous probability distributions: uniform, normal, exponential, gamma
• The DeMoivre-Laplace limit theorem and its use. "The 0.5 correction"
• Joint distribution functions, densities. Marginal densities
• Independence of random variables. Equivalent definitions: product rules for probabilities, density functions and CDFs