prac-final - STATISTICS 134 Practice Final There are 9...

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STATISTICS 134 Practice Final There are 9 questions, worth a total of 49 points. Calculations should be worked through to an explicit numerical answer. Show your work! 1. [5 points] Let U be a continuous r.v. with uniform distribution on (0 , 1). Let X = log U 1 - U . Find a formula for the density function f ( x ) of X . 2. [5 points] A box contains n tags numbered 1 , 2 ,...,n . Two tags are drawn without replacement, giving two numbers: write X for the smaller and Y for the larger number. Calculate P ( Y = X + 1). 3. [5 points] Consider Poisson random scatter with intensity λ on the plane. Let ( X,Y ) be the coordinates of the random point of the scatter which is closest to the origin. Find the joint density function f ( x,y ) of ( X,Y ). 4. [5 points] A roulette wheel has 38 slots, of which 18 are red and 18 are black. In 100 spins of the wheel, let R be the number of “reds” and let B be the number of “blacks”. Calculate the correlation cor( R,B ).
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prac-final - STATISTICS 134 Practice Final There are 9...

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