Lecture Notes For All: Introduction to Probability and Statistics



Tuesday, May 17, 2011

Introduction to Probability and Statistics

Introduction to Probability and Statistics 




Prof. Dmitry Panchenko
Figure showing the union of disjoint events.
Figure showing the union of events. (Image courtesy of Prof. Dmitry Panchenko.)

Course Features

  • Lecture notes
  • Exams (no solutions)

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

The lecture notes were taken by Anna Vetter, a student in the class.

1Probability, Set Operations(PDF)
2Properties of Probability

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


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