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概率统计(英文) chapter5 Joint Probability Distributions and Random Samples教材课程.ppt
5 Joint Probability Distributions and Random Samples;Introduction
In Chapter 3 and 4, we studied probability models for a single random variable. Many problems in probability and statistics lead to models involving several random variables simultaneously. In this chapter, we first discuss probability models for the joint behavior of several random variables, putting special emphasis on the case in which the variables are independent of one another. We then study expected values of functions of several random variables, including covariance and correlation as measures of the degree of association between two variables.
;5.1 Jointly Distributed Random Variables
The joint probability mass function for two discrete random variables
Definition: Let X and Y be two discrete random variables defined on the sample space Ωof an experiment. The joint probability mass function p(x,y) is defined for each pair of numbers (x,y) by ;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 the agency. For each type of policy, a 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.
Solution: let X=the deductible amount on the auto policy
Y=the deductible amount on the homeowner’s policy.
The joint probability table is : ;Definition: The marginal probability mass functions of X and Y, denoted by pX(x) and PY(y), respectively, are given by;Example 5.3 A bank operates both a drive-up facility and a walk-up window. On a randomly selected day,
let X=the proportion of time that the drive-up facility is in use
Y=the proportion of time that the walk-up window is in use
Let the joint pdf of (X,Y) is;Definition : The marginal probability density functions of X and Y, denote
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