First Midterm 2005

# First Midterm 2005 - AEB 6933Mathematical Statistics for...

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AEB 6933–Mathematical Statistics for Food and Resource Economics Examination I September 28, 2005 1. Given the cumulative distribution function () 32 23 7 11 1 , 36 Fxy xy x y x y =− + + defined over [ ] ,0 , 1 : a. Is this a valid cumulative distribution function? (10 points) b. Derive the marginal distribution of y . (10 points) c. Derive the conditional distribution of x given y . (15 points) d. Are x and y independent? (15 points) 2. Given that x is distributed ( ) 0,1 U and that ( ) 2 yx x = φ= for [ ] 0,1 x : a. What are the conditions required for deriving ( ) gy (the probability density function for y ) based on ( ) ? (10 points). b. Derive . (10 points) 3. The exponential distribution ( ) [ ) 0, x fx e x −γ = γ∈ Is frequently used to model arrival times (i.e., the expected time before another

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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 2005 - AEB 6933Mathematical Statistics for...

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