STAT312 Lecture : Normal sampling distributions.pdf
5 Apr 2014
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Re- has a density ( ) is invertible (i. e. increasing or decreasing, is given by call that if = ( and so 0 6= 0), then the density ( ) of. ), where with the rhs evaluated at = 1 ( ). Then the p. d. f. of y is given by is the p. d. f. of a r. vec. X 1 (i. e. ) = r (x) x). Put y 1 = h(x), (y) = (x (y)) . The following result, on the joint distribution of the sample mean and variance in normal samples, is of fundamental importance in statistics. Suppose that that x = ( 1 are i. i. d. We derive the joint p. d. f. of ( 2 ) . 1 unit vectors e to get a basis for r , and then apply gram-schmidt to get an orthonormal basis whose rst member is 1 has norm 1. This yields an orthogonal matrix h = 10.
