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Unformatted text preview: Probability and Statistics Course 92.386 Test 2 Time: 1 hour 30 minutes Please answer any five of the following six questions. Eachquestion is worth5 points Note: Numerical answers without supporting statements will not 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 denote the actualpressurefor the right tire and 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 tires are underfilled. b. Are X and Y independent? Justify your answer' 3. If thejoint probability density function of random variables X and Y is givenby:...
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