First Midterm 2000

First Midterm 2000 - 16 0.57275 0.32804 0.18788 0.10761 17...

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AEB 6933 Statistics for Food and Resource Economics Examination I 1. Given that f(x) is distributed uniform x=[0,9], derive the distribution y such that ( ) x x y = = φ . What is the expected value of () = otherwise y that such y y h 0 2 2 ? 2. Derive the moment generating function for the normal. Using the first two columns of table 1, compute the mean and variance of the normal distribution. Do the third and fourth moments conform to your expectations? Table 1. Random Distribution Observation x x 2 x 3 x 4 1 0.81327 0.66140 0.53790 0.43745 2 0.30711 0.09431 0.02896 0.00890 3 0.30947 0.09577 0.02964 0.00917 4 0.50806 0.25812 0.13114 0.06663 5 0.86261 0.74410 0.64187 0.55368 6 0.91362 0.83470 0.76260 0.69673 7 0.88713 0.78701 0.69818 0.61938 8 0.76219 0.58093 0.44278 0.33748 9 0.67116 0.45046 0.30233 0.20291 10 0.69247 0.47952 0.33206 0.22994 11 0.00259 0.00001 0.00000 0.00000 12 0.63728 0.40613 0.25882 0.16494 13 0.93605 0.87618 0.82015 0.76770 14 0.12572 0.01581 0.00199 0.00025 15 0.91023 0.82852 0.75414 0.68644
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Unformatted text preview: 16 0.57275 0.32804 0.18788 0.10761 17 0.14420 0.02079 0.00300 0.00043 18 0.35242 0.12420 0.04377 0.01543 19 0.34554 0.11939 0.04126 0.01426 20 0.71490 0.51108 0.36537 0.26120 21 0.23511 0.05528 0.01300 0.00306 22 0.22770 0.05185 0.01180 0.00269 23 0.41264 0.17027 0.07026 0.02899 24 0.78597 0.61775 0.48554 0.38162 25 0.24312 0.05911 0.01437 0.00349 Sum 13.37330 9.17074 6.97880 5.60038 3. Given the joint distribution function ( ) ( ) y x x y x f + = 2 7 12 , over the range x,y=[0,1]: Are the random variables x and y independent? 4. Given the covariance matrix = = 3 1 1 5 22 21 12 11 Find the conditional variance of 11 given the value of x 2 . 5. Given that the probability of a heads in a coin toss is .4 and letting heads=1, what is the expected value and the variance of 25 coin tosses?...
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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First Midterm 2000 - 16 0.57275 0.32804 0.18788 0.10761 17...

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