MidTermTest1VersionCSolution

MidTermTest1VersionCSolution - CHEN3010 Version C Applied...

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CHEN3010 Applied Data Analysis Fall 2004 Version C Mid Term Test 1 Name:____________________ Answer each question on its own sheet and use the reverse side if necessary. Staple all seven questions together, in the right order, if you separate the question sheets. Open Book, Notes, and Workshops. Calculators allowed, but you can not borrow one. 75 minutes, 75 points, 7 problems, 3 different versions Problem 1 (10 points) Given the historical data on hurricanes making a landing at an average of 2.3 per year, what is probability that a month will elapse with no hurricanes? Solution: Number of hurricanes over a continuous period is a discrete random variable following a Poisson process. Hence, it follows a Poisson distribution. The average number of hurricanes per month λ == 23 12 0 19166 . .# / month P[X=0] = e = 0 0 0 82558 ! . For no hurricanes in a month, the problem can also be solved using the exponential distribution that governs the continuous random variable Y of the time interval between subsequent hurricanes. fy e y () = Probability that a month will elapse with no hurricanes: PY e dy e e e yy [] . . >= = = −− 10 0 82558 1 1 0 191666 λλ
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CHEN3010 Applied Data Analysis Fall 2004 Version C Mid Term Test 1 Name:____________________ Problem 2. (10 points) Let X denote the amount in kilogram of polyurethane cushioning found in a car. The probability density for X is fx x x k () ( ) / = 60 2 2 for 10 < x < 20.
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MidTermTest1VersionCSolution - CHEN3010 Version C Applied...

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