Prob/Stat&Mathematica
Draft
Authors: Bruce Carpenter, Bill Davis and Jerry Uhl ©1999
Producer: Bruce Carpenter
Publish er:
Distributor: ![]()
Estimating probabilities and measurements by Monte Carlo simulation
Frequency, cumulative distribution functions and histograms for data sets of numbers.
Expected value and variance for data sets and functions of data sets .
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.
Markov's inequality, Chebyshev's inequalities and standard deviation. Law of large numbers. Random Walks, Outliers
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
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.
Joint distributions: Discrete and Continuous. Independence, Conditional probability and conditional expectations. Corellation.
Central limit theorem. Generatng functions. Special attention to sums of independent normal and exponential randon variables.
Permutations, combinations, Bernoulli,Binomial and Poisson distributions. Approximations by normal distributions
Sampling for the mean and variance. Acceptance testing.
C&M calculus has made me understand Economics and actually like it. Most people cringe when they hear that I am an Econ major, and I think their reaction results from the fact that they really don't understand it. Never have I used complex equations in Economic applications, but what I have learned visually from C&M calculus helps me understand graphs and concepts inclass everyday. This comprehension has made me realise the incredible logic behind economics, and now the subject fascinates me.
Techs support both the lab machines and the software used in this program.
In the event of a problem, send an e-mail to tech@cm.math.uiuc.edu.