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E.2.0.solved - Economics 390 Midterm#2 Page 1 Economics 390...

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Economics 390, Midterm #2 Page 1 Economics 390 Midterm #2 180 Points 2 Hours 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. Suggestions: There are 18 questions, and I expect them to take on average 5 minutes each, or approximately 90 minutes total. 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) If X and Y are statistically independent random variables, does this imply that their correlation coefficient (ρ) equals exactly 0? Yes or no, and concisely explain why . (A correct explanation exclusively determines grade.) Yes. Intuitively, if the value of one variable has no relation to the value of the other, as is meant by SI, they can’t possibly be correlated. The best way to show this (but is not essential for credit if you demonstrate the correct intuition), is to start with the definition of covariance: ( , ) ( )( ) ( , ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) 0*0 0 0 X Y X Y x y x y X Y x y Cov X Y x y P x y x P x y P y x P x y P y μ μ μ μ μ μ ρ = - - = - - = - - = = = ∑∑ ∑∑ We are able to separate the two because by independence P(x,y)=P(x),P(y). 2. (10 points) Suppose that two random variables, X and Y, have a covariance of -0.5 and a correlation coefficient (ρ) of -0.8. Additionally, the variance of X is 1. What is the standard deviation of Y? ( , ) .5 .5 .8 .625 .8 1* Y X Y Y Cov X Y ρ σ σ σ σ - - = → - = = = - 3. The owners of the White Castle fast food chain are interested in the relationship between hamburger and french fry consumption. The table below is a partial reconstruction of the joint distribution of customer’s orders of burgers (B) and fries (F).
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