STOR 435: Introduction to Probability


Study Guide for Midterm 2


1. Basic definition of a continuous random variable, probability density function

2. Relationship between pdf and CDF

3. Expectations and Variance, basic properties

4. Expectations of functions of a r.v., and formula for expectation in terms of P(X > x)

5. Basic continuous random variables: densities, CDFs, expectations, variances
     a. Uniform
     b. Normal (finding normal probabilities using tables)
     c. Exponential (memoryless property)
     d. Gamma family of distributions, and the Gamma function
     e. Cauchy
    
6. The CDF method

7. The normal approximation to the binomial

8. Jointly distributed random variables

9. Joint pmf and pdf.  Relationship between joint and marginal distributions

10. Finding probabilities involving two jointly distributed continuous r.v.

11. Basic multivariate calculus

12. Independent random variables: definition, connections with joint pmf and joint pdf

13. Sums of independent random variables: Poisson, Gamma, Normal, Binomial

14. Conditional distributions: Definitions and properties of conditional pmf, pdf