E-1.2.0.solved

E-1.2.0.solved - Economics 390, Midterm #2 Page 1 Economics...

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Economics 390, Midterm #2 Page 1 Economics 390 Midterm #2 180 Points 75 Minutes Instructions: Answer the following questions as clearly as you can. Circle your answers . Also, show your work. You do not need to write out every detail, but give a clear indication of how you are making your calculations. This is for your benefit, as we can give partial credit if, say, you make a mistake early in the problem that otherwise would make a correct final answer wrong. You may use any type of hand-held calculator. All other electronic devices are prohibited. Several question I consider to be a little more challenging than the others. I’ve identified these with an asterisk *. Suggestions: There are 18 problems. Do not get stuck on any one problem. The questions vary in difficulty, and you should be sure to get done the ones you feel strong about. The most difficult part of any question is going to be determining where the question fits into the class as a whole . If you can do that, and you understand the formulas in the formula sheet, then translating the problem into the formulas and executing the calculations is going to be relatively straightforward. Name: ___________________________________ ID: ___________________________________
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Economics 390, Midterm #2 Page 2 1. (10 points) Consider two random variables X and Y, where Cov(X,Y)>0. Then, all else equal, when the standard deviation of X increases, the correlation coefficient ρ also increases. True or False, and explain your answer. (Explanation exclusively determines grade.) False. ( , ) X Y Cov X Y ρ σ σ = . If σ X increases, then ρ must fall. 2. (10 points) Consider two continuous distributions for the random variables R and S. R has a PDF given by the function f R (R), and S has a PDF given by the function f S (S). If f R (1)>f S (1), then the probability that R=1equals the probability that S=1. True or False, and explain your answer. (Explanation exclusively determines grade.) True. The key here is the fact that for a continuous RV, as opposed to a discrete RV, the probability that the RV takes on any particular value is exactly 0, regardless of the value of the PDF. Thus, P(R=1)=P(S=1)=0. 3.
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E-1.2.0.solved - Economics 390, Midterm #2 Page 1 Economics...

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