MATH 340, Study Guide for Midterm Test 2

4/27/2013

Test coverage

5. Continuous Random Variables
   1. Introduction: concept of probability density (5.1)
   2. Expectation and Variance (5.2)
   3. The uniform random variable (5.3)
   4. Normal random variables (5.4)
   5. The normal approximation of the binomial distribution (5.4.1)
   6. Exponential random variables (5.5)
   7. Skip: 5.5.1 to end of the chapter, except 5.6.1
6. Jointly distributed random variables
   1. Joint distribution functions (6.1)
   2. Independent random variables (6.2)
   3. Sums of independent random variables (6.3)
   4. Skip: 6.4 to end of the chapter
7. Properties of expectation
   1. Introduction (7.1)
   2. Expectations of sums (7.2)

Key concepts

• Probability density, the cumulative distribution function
• Expectation, variance; expectation of a function of a random variable
• Continuous probability distributions: uniform, normal, exponential, gamma
• Discrete probability distributions: Bernoulli, binomial, Poisson
• The DeMoivre-Laplace limit theorem and its use
• Joint distribution functions, densities. Marginal densities
• Independence of random variables. Equivalent definitions: product rules for probabilities, density functions and CDFs
• Convolution of density functions and the way to compute density for the sum
• Computing density for other combinations of random variables (XY, X/Y,...) using CDF
• Expectations, variances applied to the case of several random variables