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Statistical Inference (chapter 4 (multivariate model (n-dim random…

- - - - discrete bivariate ramdom vector
        
        joint pmf
        
        pmf is nonnegative
        
        marginal pmf
        
        probability of event
        
        function of expectation
        
        linearity of expectation
        
        conditional pmf
      - continuous bivariate random vector
        
        joint pdf
        
        marginal pdf
        
        joint cdf
        
        fundamental theorem of calculus
        
        function of expectation
        
        conditional pdf
        
        conditional expectation
        
        conditional variance
        
        a random variable
      - independence
        
        p153 lemma
        f(x,y) = g(x)h(y)
        
        p154 defined on cross product AxB
        
        expectation
        
        p155 theorem
        
        moment generating functions
        
        p155 theorem
        
        p156 exception for continuous r.v.
      - bivariate transformation
        
        discrete bivariate
        
        continuous bivariate
        
        p158 jacobian
        
        p161 theorem
        still independent after transformation of independent variables
      - p164 theorem
        expectation of conditional expectation
        
        p167 theorem
        variance by condition
      - covariance
        
        correlation
        
        p171 theorem
        independence
        
        p172 theorem
        linearity
        
        p170 theorem
        formula
        
        p171 theorem
        linear combination of vairance
        
        bivariate normal
      - multivariate distribution
        
        everything related to two dimensional random vector
        
        mutinomial distribution
        
        marginal pmf
        
        p181 theorem
        multinomial theorem