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# PROBABILITY MATH 511

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This 2 page Class Notes was uploaded by Cassidy Grimes on Monday October 26, 2015. The Class Notes belongs to MATH 511 at University of South Carolina - Columbia taught by J. Tebbs in Fall. Since its upload, it has received 39 views. For similar materials see /class/229537/math-511-university-of-south-carolina-columbia in Mathematics (M) at University of South Carolina - Columbia.

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Date Created: 10/26/15

STATMATH 5 1 1 OVERVIEW STAT 5 12 J TEBBS Here is a summary of some of the main ideas from the prerequisite STATMATH 511 Probability WMS stands for Wackerly Mendenhall and Schaeffer text Chapter 1 WMS Overview of basic statistics We skipped this chapter STAT 110 Chapter 2 WMS Basic probability theory set notation Kolmorogov axioms com plement rule tools for counting eg combination permutation etc conditional probability Law of Total Probability Bayes Rule Chapter 3 WMS Discrete random variables positive probability is assigned to spe ci c points probability mass functions pmf means and variances of discrete random variables moment generating functions Bernoulli trials lmportant discrete models H Discrete uniform Equal probability assigned to each support point P Binomial bnp Bernoulli n 1 Number of successes out of n Bernoulli trials 9 Geometric geomp Number of Bernoulli trials until 1st success 7 Negative binomial nibrp Number of Bernoulli trials until the rth success gen eralisation of the geometric U Hypergeometric hyperN n 7 Number of Class 1 objects selected from 7 Finite population version of the binomial 03 Poisson Poisson Records counts in a Poisson process over time or space Chapter 4 WMS Continuous random variables positive probability is assigned to intervals not speci c points probability density functions pdf cumulative distribution functions cdf means and variances of continuous random variables moment generating functions Chebyshev lmportant continuous models 1 Uniform U0102 Pdf is constant over the interval from 91 to 02 2 Normal NW 02 Most widely used probability model EY M and VY 02 Symmetric unimodal bell shaped7 PAGE 1 STATMATH 5 1 1 OVERVIEW STAT 5 12 J TEBBS 9 Gamma gammaoz Popular model for random variables with positive support Shape parameter a scale parameter 6 Skewed right in general 4 Exponential exponential A gamma distribution with 04 1 Exponential decay shaped pdf 9 X2 X2V A gamma distribution with 04 V2 and B 2 Degrees of freedom parameter V Popular model in applied statistics 03 Beta betaoz Support over 01 Very exible model for proportions 5 Other named77 distributions Cauchy Weibull log normal Pareto etc Chapter 5 WMS Random vectors multivariate distributions particular attention paid to bivariate distributions joint pmfs and pdfs marginal distributions conditional distributions independence multivariate expectations covariancecorrelation multino mial distribution bivariate normal conditional expectations iterated rules for mean and variance Going forward It will be helpful to know all of the named discretecontinuous dis tributions that we discussed in STATMATH 511 their pmfspdfs means variances and moment generating functions Recall that the cumulative distribution function for a random variable Y is given by Fyy PY S Useful integral shortcuts For 04 gt 0 and B gt 0 recall that freer ew New and 0 ya l 7 w ldy These facts follow from the properties of gamma and beta pdfs respectively Recall that the gamma function Us satis es Us s 71Ps 7 1 for s gt 1 PAGE 2

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