Stat400Lec13(Ch4.1) - STAT 400 Chapter 4.1 Spring 2012...

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STAT 400 Chapter 4.1 Spring 2012 Chapter 2- 3: Univariate distirubitons (Review) Discrete r.v. o Uniform discrete, hypergeometric, bernoulli, binomial, poisson , negative binomial Continuous r.v. o Uniform, cauchy, exponential, gamma, chi-square, normal (gaussian) Important Statistics: o Mean, variance, standard deviation, moment generating function, median Distribution: o p.m.f. c.d.f (discrete) o p.d.f c.d.f (continuous) Chapter 4: Bivariate distributions Let X and Y be two discrete random variables. 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 P ( ( X, Y ) A ) =       y x A y x p , , . Let X and Y be two continuous random variables. Then f ( x , y ) is the joint probability density function for X and Y if for any two-dimensional set A P ( ( X, Y ) A ) =    A dy dx y x f , . Joint p.m.f. for two discrete r.v.s. joint p.d.f for two continuous r.v.s.
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1. Consider the following joint probability distribution p ( x , y ) of two discrete random variables X and Y: x \ y 0 1 2 1 0.15 0.10 0 2 0.25 0.30 0.20 Is this a valid probability model? a)
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Stat400Lec13(Ch4.1) - STAT 400 Chapter 4.1 Spring 2012...

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