slides_4_ranvecs

# Where the second to last equality follows from the

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where the second-to-last equality follows from the independence of X 1 ,..., X m and the last inequality again follows from the definition of g j 1  . 31

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EXAMPLE : Suppose X and Y 0 are independent. Then X and log Y are independent, as are exp X and log Y , and X 2 and 1/ Y , and so on. 32
3 . Moments Involving Random Vectors Computing moments of random vectors, and functions of them, is very important in economics and econometrics. Let X be a random vector of dimension m , and let g : X be a real-valued function defined on the range of X , X m . Then, of course, Y g X is a random variable. In principle, given the CDF or PDF of X we can derive the distribution of Y . 33

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