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Basic Concepts
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Introductory Probability: Statistics 116
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Some Puzzles to think
Lecture Summaries
Basic Concepts
Probability
Sample Space 09/24
Matlab Dice Example from lecture 09/24/98
Definition of Probability 9/25
Discrete Uniform Random Distribution
Computer Simulation
Problem Session,09/25/98: De Méré's Problem
Another Matlab Example for dice game
Set Facts, Venn Diagrams 9/28
Properties of Probabilities 9/28
Tree Diagrams
Determination of probabilities 9/29
Infinite Sample Spaces 9/29
Continuous random variables 9/30
Examples
Monte Carlo Procedures for computing areas 9/30
Buffon's Needle - 9/30
Densities 10/2
Examples with simulations 10/2
Cumulative Distribution Function 10/5
Examples with functions of Uniform Random Numbers 10/5
Combinatorics
Enumeration Rules
Birthday Problem 10/6
Approximating
n
! 10/7
A note on doing symbolic computations
More about k-subsets 10/9
The matching Problem 10/9
Multinomial Coefficients and applications 10/12
Conditional Probability
Definition and Properties 10/12
Conditional Probability IS a probability 10/12
Examples of using conditional probability 10/13
Monty Hall 10/14
Independence 10/14 and 10/16
Independence of more than two events 10/20
The Craps principle 10/16
Example of computation for craps 10/19
Joint Distributions 10/19, 10/20
Gambler's Ruin 10/21
Joint Probability Distribution for
n
variables 10/21
Conditionning with continuous random variables
Jointly Distributed random Variables 10/26
Continuous Random Variables 10/26
Marginal Distributions10/26
Examples10/26
Independent Random Variables 10/26
Independence for Continuous Random Variables 10/27
Conditional Distributions 10/27
Conditional Density 10/28
Bayes Billiard Balls 10/28
Beta Random Variable 10/28
Order Statistics 10/30
Example with a Uniform Random Variable
Special Distributions
Binomial Distribution 10/29
Odds Ratios and Mode 10/30
Hypergeometric Random Variable 11/3
Geometric 11/3
Negative Binomial 11/3
Poisson random variable 11/2
Motivation
Definition 11/2
Parameters of Distributions 11/3
Special Continuous Distributions 11/2
Change of Variables 11/3
Exponential Random Variable 11/4
Normal Random Variables 11/4
Standard Normal Random Variable
Normal Random Variable
How was the constant
found?
Expectation and Variance 11/6
Discrete Random Variable 11/6
Properties of Expectation 11/6
Pascal's rationalisation of religion
Indicator variables and Bernouilli variables
Examples of computing expectations of sums 11/9
Conditional Expectation 11/9
Variance 11/10
Conditional Expectation
Expectations and Variances for Continuous Random Variables 11/16
Properties
Variance 11/17
Special Lecture:11/18: Persi Diaconis on ESP
Sums of Random Variables 11/23
Discrete CAse
Sum of Poisson independent 11/24
Sums of Continuous Random Variables
Gamma density
Sum of two independent Normal random variables 11/25
Limit Theorems
Chebychev's Inequality
Weak Law of Large Numbers
The Central Limit Theorem
Polar Method for Generating Normal Random Variables 12/2
Web sites for the central limit theorem
Susan Holmes
1998-12-07
found?