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Unformatted text preview: X ∼ N ( μ x , Σ ) , what is the distribution of AX + b , where A and b are conformable matrices of contants? 8. For a random vector X ∼ N ( μ x , Σ ) , what is the distribution of ( X-μ x ) Σ-1 ( X-μ x ) ? 9. Using Octave, write a little program that veri²es that Tr ( AB ) = Tr ( BA ) for A and B con-formable matrices of random numbers. Note: there is an Octave function trace. Note that checking equality using the Octave operation ” == ” will indicate that they are not equal (though in fact they are). Why is that? 10. For the model with a constant and a single regressor, y t = β 1 + β 2 x t + e t , which satis²es the classical assumptions, prove that the variance of the OLS estimator declines to zero as the sample size increases. 1...
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This note was uploaded on 09/12/2010 for the course GERAS 099876f taught by Professor Gtewewa during the Spring '09 term at Aberystwyth University.
- Spring '09