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