Test_1_1999 - is positive(20 2 Exercise 5.4.8 3 Suppose X...

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Department of Economics Professor Dale J. Poirier University of California, Irvine November 2, 1999 MIDTERM TEST ECON 220A Statistics and Econometrics I (open book) Directions : You must answer each of the following questions. Points (out of 100) are allocated as noted to the left of each question. Allocate your time according to these points. To receive any partial credit, you must show your work. Results from the text need not be reproduced in detail - you can merely cite the source. (20) 1. A laboratory blood test is 95 percent effective in detecting a certain disease when it is, in fact, present. However, the test also yields a “false positive” result for one percent of the healthy persons tested. If .5 percent of the population actually has the disease, what is the probability that a person has the disease given that her test result
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Unformatted text preview: is positive? (20) 2. Exercise 5.4.8 3. Suppose X γ (c, d) and Z X = x N K ( θ , x-1 Ω ), where c > 0, d > 2, θ is a K×1 vector and Ω is a K×K positive definite matrix (all assumed known). Define Q = X(Z AZ), where A is a known K×K positive definite matrix. (15) (a) Find E(Q). (15) (b) Find Var(Q). [Hint: consider Exercise 3.4.35(b).] 2 Σ 1 ρ yx ρ yz ρ yx 1 ρ xz ρ yz ρ xz 1 . 4. Suppose Y, X and Z have a trivariate normal distribution with zero means and covariance matrix Define U = Y - ρ yx X. (10) (a) Find the conditional distribution of U, given X and Z. (10) (b) Is U mean-independent of X? (10) (c) Is U mean-independent of Z?...
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