Introduction to Probability and Statistics Lectures

Course Description

This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression.

Lecture Notes

LEC #	TOPICS	LECTURE NOTES
1	Probability, Set Operations	(PDF)
2	Properties of Probability Finite Sample Spaces, Some Combinatorics	(PDF)
3	Multinomial Coefficients, Union of Events	(PDF)
4	Matching Problem, Conditional Probability	(PDF)
5	Independence of Events	(PDF)
6	Solutions to Problem Set 1	(PDF)
7	Bayes' Formula	(PDF)
8	Random Variables and Distributions	(PDF)
9	Cumulative Distribution Function	(PDF)
10	Marginal Distributions	(PDF)
11	Conditional Distributions, Multivariate Distributions	(PDF)
12	Functions of Random Variables, Convolution	(PDF)
13	Functions of Random Variables: Sum, Product, Ratio, Maximum, Change of Variables	(PDF)
14	Linear Transformations of Random Vectors, Review of Problem Set 4	(PDF)
15	Review for Exam 1	(PDF)
16	Expectation, Chebyshev's Inequality	(PDF)
17	Properties of Expectation, Variance, Standard Deviation	(PDF)
18	Law of Large Numbers, Median	(PDF)
19	Covariance and Correlation, Cauchy-Schwartz Inequality	(PDF)
20	Poisson Distribution, Approximation of Binomial Distribution, Normal Distribution	(PDF)
21	Normal Distribution, Central Limit Theorem	(PDF)
22	Central Limit Theorem, Gamma Distribution, Beta Distribution	(PDF)
23	Estimation Theory, Bayes' Estimators	(PDF)
24	Bayes' Estimators	(PDF)
25	Maximum Likelihood Estimators	(PDF)
26	Chi-square Distribution, t-distribution, Confidence Intervals for Parameters of Normal Distribution	(PDF)
27	Confidence Intervals for Parameters of Normal Distribution	(PDF)
28	Review for Exam 2	(PDF)
29	Hypotheses Testing, Bayes' Decision Rules	(PDF)
30	Most Powerful Test for Two Simple Hypotheses	(PDF)
31	t-test	(PDF)
32	Two-sample t-test, Goodness-of-fit Tests, Pearson's Theorem	(PDF)
33	Simple Goodness-of-fit Test, Composite Hypotheses	(PDF)
34	Contingency Tables, Tests of Independence and Homogeneity	(PDF)
35	Kolmogorov-Smirnov Goodness-of-fit Test	(PDF)
36	Review of Test 2	(PDF)
37	Review for the Final Exam	(PDF)

Exams and Solutions

PRACTICE TESTS                 SOLUTIONS

Practice Test 1 (PDF)             (PDF)

Practice Test 2 (PDF)             (PDF)

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