MATH 447. Introduction to Probability and Statistics I.

The list of topics below is the minimum that will be covered in the course. The time schedule that appears below that will be followed as closely as possible. A common final wil be given in all sections of the course.

List of topics

BOOK: Mathematical Statistics with Applications by D. Wackerly, W. Mendenhall lII and R. L. Scheaffer, Fifth edition. Duxbury Press.

The numbers in parenthesis refer to section numbers in the book.

1. Introduction to Statistics (1.1-1.5)
2. Introduction to Probability (2.2)
3. Review of set notation (2.3)
4. Discrete probabilities (2.4)
5. The sample point method for finding the probability of an event (2.5)
6. Tools for counting sample points (2.6)
7. Conditional probability (2.7)
8. Independent events (2.7)
9. Laws of probability (2.8)
10. The event decomposition method for finding the probability of an event (2.9)
11. The total law of probability and Bayes' formula (2.10)
12. Random variables (2.12)
13. Probability distribution for a discrete random variable (3.2)
14. Expected value of a random variable or a function of a random variable (3.3)
15. Binomial distribution (3.4)
16. Geometric distribution (3.5)
17. Negative binomial distribution (3.6)
18. Hypergeometric distribution (3.7)
19. Poisson distribution (3.8)
20. Moments and moments generating functions for discrete random variables (3.9)
21. Tchebysheffs's inequality for discrete random variables (3.11)
22. Distribution of a continuous random variable (4.2)
23. Expected value of a continuous random variable (4.3)
24. Uniform distribution (4.4)
25. Normal distribution (4.5)
26. Gamma distribution (4.6)
27. Beta distribution (4.7)
28. Moments and moments generating functions for continuous random variables (4.9)
29. Tchebysheffs's inequality for continuous random variables (4.10)
30. Bivariate and multivariate distributions (5.2)
31. Marginal and conditional distributions (5.3)
32. Independent random variables (5.4)
33. Expected value of a function of random variables (5.5-5.6)
34. Covariance of two random variables (5.7)
35. Expected value and variance of linear functions of random variables (5.8)
36. Multinomial distribution (5.9)
37. Bivariate normal distribuion (5.10)
38. Conditional expectations (5.11)
39. Finding the density of a function of random variables (6.2)
40. Method of distribution functions (6.3)
41. Method of transformations (6.4)
42. Method of moment generating functions (6.5)
43. Order statistics (6.6)
44. Sampling distributions for normal data (7.2)
45. Central limit theorem (7.3-7.5)