概率与统计（英文）chapter 51 Joint Probability Distributions and Random Samples.pptVIP

Chapter 5 Joint Probability Distributions and Random Samples 5.1 Jointly Distributed Random Variables 5.2 Expected Values,Covariance,and Correlation 5.3 Statistics and Their Distributions 5.4 The Distribution of the Sample Mean 5.5 The Distribution of a Linear Combination Supplementary Exercises Bibliography 5.1 Jointly Distributed Random Variables There are many experimental situations in which more than one random variable(rv) will be of an investigator.We shall first consider joint probability distributions for two discrete rv’s,then for two continuous Variables,and finally for more than two vaeiables. The Joint Probability Mass Function for Two Discrete Random Variables The probability mass function(pmf) of a single diacrete rv X specifies how much probability mass is placed on each X value.The joint pmf of two discrete rv’s X and Ydiscribes how much probability mass is placed on each possible pair of values(x,y). DEFINITION Let X and Y be two dicrete rv’s defined on the sample space of an experiment.The joint probability mass function p(x,y) is defined for each pair of numbers (x,y) by p(x,y)=P(X=x and Y=y) Let A be any set consisting of pairs of (x,y) values.Then the ptobability is obtained by summing the joint pmf over pairs in A: Example 5.1 A large insurance agency services a number of customers who have purchased both a homeowner’s policy and an automobile policy from agency.For each type of policy,deductible amount must be specified .For an automobile policy,the choices are $100 and $250, whereas for a homeowner’s policy the choices are 0, $100,and $200. Suppose an individual with both types of policy is selected at random from the agency’s files.Let X=the deductible amount on auto policy and Y=the deductible amount on homeowner’s policy.Possible(X,Y) pairs are then(100,0),(100,100),(100,200),(250,0),(250,100),and(250,200);the joint pmf specifies the probablity associated with each one of these pairs, with any othe