Test 2 & Solutions

# Test 2 & Solutions - Probability and Statistics Course...

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Probability and Statistics Course 92.386 Test 2 Time: 1 hour 30 minutes Please answer any five ofthe following six questions. Eachquestion isworth5 points Note: Numerical answers without supporting statements willnot be given credit. 1. A coin is biased so that heads is twice as likely to occur as tails. For 3 independent tosses of the coin, a. determine the probability distribution function (Pdf) of the random variable X, the total number of heads b. find the probability of getting at mosttwo heads 2. Each tile of an experimental airplane is supposed to be filled to a pressure of 4Opsi" Let X denotethe actualpressurefor the righttireand Y denote the actualpressurefor the lefttire, SupposeX and Y are random variables withjoint density given by: fx,y (x, y) = k (x 2 '·I ); 30 <x < 50, 30<y < 50 a. Findthe probability that both tiresare underfilled. b. AreX and Y independent? Justify your answer' 3. If thejoint probability density function of random variables X andY isgivenby: fx,y (x, y) = 24 Y (l-x-y); for 0 < x < 1, 0 <y < 2 and0 elsewhere, It;

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• Fall '05
• JUNG
• Statistics, Probability, Probability distribution, Probability theory, 1 Hour, probability density function, 30 Minutes

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