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Math 461

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Prob/Stat&Mathematica
Draft
Authors:  Bruce Carpenter, Bill Davis and Jerry Uhl  ©1999
Producer:  Bruce Carpenter
Publish er:         Distributor:  

Syllabus

Prob.01 Monte Carlo simulations

Estimating probabilities and measurements by Monte Carlo simulation

Prob.02 Data Analysis

Frequency, cumulative distribution functions and histograms for data sets  of numbers.
Expected value and variance for data sets and functions of data sets .

Prob.03 Probabilities

Probabilities of unions and intesections of data sets. Conditional probability and independence.
Series wiring versus parallel wiring.  Drug testing. Birth day problem.    Probability of winning at craps. Gambler's ruin.

Prob.04 More data analysis

Markov's inequality, Chebyshev's inequalities  and standard deviation.  Law of large numbers. Random Walks, Outliers

Prob.05 Normal and Exponential

Normal distribution and the bell curve.  Exponential distribution and the   exponential curve.Recognizing data sets that are approoximately nor mally or exponentially distributed. The memoryless property of the exponential distribution. Monte Carlo generation of normally or exponentially distributed   data sets.  Experiments with sample averages and the normal distribution

Prob.06 Random variables

Continuous versus discrete random variables. Approximation of continuous random variables by   discrete random variables. Probability density functions a nd cumulative distribution functions. Brand name continuous distributions: Uniform, normal,exponential, Weibull, chi-square,gamma and beta. Sample uses of each. Monte C arlo generation of data sets following a specified distribution.

Prob.07 Joint distributions

Joint distributions: Discrete and Continuous. Independence, Conditional probability and conditional expectations. Corellation.

Prob.08 Generating functions and the Central Limit Theorem

Central limit theorem. Generatng functions. Special attention to sums of independent normal and exponential randon variables.

Prob.09 Counting

Permutations, combinations,  Bernoulli,Binomial and Poisson distributions. Approximations by normal distributions

Prob.10 Statistics

Sampling for the mean and variance. Acceptance testing.

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