ECON 705 Midterm: 705_prelim
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Friday june 6, 2014 time limit: 150 minutes. Instructions: (i) the exam consists of two parts. E[xy ] = e[x]e[y ] implies that the random variables x and y are independent. Explain your answer. (ii) (3 points) consider the regression yi = (cid:18)xi + ui, where xi is scalar. The larger (cid:27)2, the more precise is the ols estimator. Explain your answer. (iii) (3 points) suppose that x is a random variable with cdf fx (x). Then the transformed random variable y = fx (x) (cid:24) U [0; 1], where u [0; 1] is the uniform distribution on the unit interval. Explain your answer by deriving the distribution of y . Consider the model given by the conditional distribution y j(cid:18) (cid:24) n ((cid:18); 1) and the marginal distribution (cid:18) (cid:24) n (0; 1=(cid:21)). Note that the sample size is n = 1. This question involves three di erent estimators of (cid:18), denoted by ^(cid:18)b, ^(cid:18)(cid:3), and ^(cid:18)mle.
