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# Introduction To Probability Models STAT 22500

Purdue

GPA 3.63

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This 3 page Study Guide was uploaded by Bailey Macejkovic on Saturday September 19, 2015. The Study Guide belongs to STAT 22500 at Purdue University taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/207945/stat-22500-purdue-university in Statistics at Purdue University.

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Date Created: 09/19/15

Stat 225 Topics for Exam 2 To study for Exam 2 practice the following skills will be helpful This list is not exhaustive and is only meant as a guide to help you study 0 Random Variables gt gt V Understand the difference between Event and Random Variable Know the difference between discrete and continuous random variables Be able to write down the PMF table for a random variable described in a story problem make sure that your probabilities add up to one Graph PMFs in form of histograms Compute probabilities and conditional probabilities using the Fundamental Probability Formula for a random variable with given PMF 0 Expected value Variance gt V V Compute expected values of a random variable from the PMF table or from a Histogram Know the basis properties of expected value EaX b aEX b Definition of variance and standard deviation and how to compute them Basic properties of variance both for dependent and independent random variables 0 You should be familiar with the Bernoulli Binomial Hypergeometric Geometric Negative Binomial and Poisson distributions gt V For a random variable described in words X of you should be able to identify its distribution and determine the values of all relevant parameters In problems asking you to compute a probability expected value or variance for a story problem you may have to define the random variable in words yourself X of and identify its distribution along with all relevant parameters and then rephrase the question in probability notation and use the appropriate formulas to find the solution Here are some facts that you should be aware of concerning the above distributions gt The sum of n independent Bernoulli trials has a Binomialn p distribution gt Binomial approximation to the Hypergeometric is appropriate if N gt 2017 gt Lackof Memory property of the Geometric distribution PXnlegtnPXc gt Computing tail probabilities for a geometric random variable PX gt n l p gt The sum of r independent Geometric p random variables has a Negative Binomialr p distribution gt Poisson approximation for the Binomial is appropriate if N gt100 and p lt 001 In this case A np gt The sum of two independent Poisson 11 and Poisson AZ random variables has a Poisson 11 12 distribution Bivariate Distributions gt Understand what the joint probability mass function p N x y is and how to obtain one from a story problem gt Compute the marginal distributions of both random variables involved gt Compute expected values and variance for both random variables gt Compute covariance and correlation of the two random variables Know what these quantities measure gt The concept of independence and how to check from a given joint PMF table whether or not the random variables are independent gt You should be able to compute conditional probabilities e g PX gt 4 Y 1 and probabilities like eg PX Y gt 4 from a givenjoint PMF table gt Compute the variance of a linear combination of random variables that are not independent e g Var2X 3Y Continuous Random Variables V V VV Probability Density functions PDFs I Know the conditions a PDF must satisfy I Be able to sketch a PDF Cumulative Density functions CDFs I Know how to compute a CDF from a PDF I Know how to compute the PDF from a CDF I Know the definition of CDF Know how to compute probabilities using either the PDF or the CDF and know how to read the probabilities from a PDF or CDF graph Know how to compute the expected value and variance from a PDF Know how to compute the median or other percentiles from a given PDF or CDF

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