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First Midterm 1999

# First Midterm 1999 - 19 0.6637 20 0.7892 3 Given(X,Y such...

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AEB 6533–Stastistics in Food and Resource Economics First Test–October 6, 1999 1. Assume f(x)=1/10 and y=ln(x), find g(y), E[y], and V[y]. 2. Is f(x)=3x 2 a valid distribution function? Find the moment generating function for this distribution. Given the sample below, do the first three sample moments agree with what you expect? Observation x 1 0.9154 2 0.0720 3 0.6965 4 0.9528 5 0.6044 6 0.7113 7 0.6163 8 0.4971 9 0.3148 10 0.5633 11 0.0317 12 0.4200 13 0.6522 14 0.9747 15 0.7210 16 0.1208 17 0.3644 18 0.4458
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Unformatted text preview: 19 0.6637 20 0.7892 3. Given (X,Y) such that V(X)=V(Y)=1, E[X]=1, E[Y]=2, and Cov(X,Y)=1, what is the estimated value of Y given X=0 using the minimum variance estimator? 4. What is the expected value and variance of a gamble of five coin tosses (assume that probability of a head is .5) where each head pays \$1? What is the probability that there will be less than three heads? 5. Demonstrate that X and Y are not independent if f(x,y)=4x-4xy for 0<x<1 and 0<y<1....
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