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Unformatted text preview: STAT 2611: Mathematical Statistics, University of MinnesotaMorris
I Midterm Exam 3 04/16/2010 ' NAME: K Student ID: Problem I. Let Y have a normal distribution with mean 10 and variance 4. Find P(Y< 6.28) and P(4<Y<l6). (l0 pts) : P( ~3.o<z 49.0)
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hours. A sample of n=5 identical components is taken. Assuming independence among the components,
~ what is the probability that at least one fails hefore 200 hours? (10 pts) w W” "1/;
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(y) {l—e" , yZO. FindP(Y>110Y5200).(10pts) POM) 0' 5)“), Pu) , FUJ)
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l, 6,4 0“}?lbmi $13 Pmlem 4. Let Y be disuibhtcd as f( y) , where f(y) =cy2e""‘.for y> 0:f(y) = 0. yso. Find the value of c that makes f (y) a density function. (10 pts) ' 13M Carma “1 *9 *0” Problem é. , Y 2 ,..., Y“, are independent, identical distributed as Beta(2,l). (a) What is the probability density function of Y , the 6"1 order statistic? (10 pts)
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’ i d ° PM t ’ yo ’2 t— 5?) (alto5%) W/ Problem 6. We have n=1000 parts; each is defective with probability 0.10 (p). What is the probability that _ 120 or more are defective? (10 pts)
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Problem 7. Yl , Y 2 ,..., Y" are independent, identical distributed as N (/1, 0':2 The sampling distn'bution — l " 0' 2
of Y = — z Y, is N [ ,u, ——J . Prove this by Moment Generating Function Method. (20 pts)
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 Spring '10
 FROHMADER
 Normal Distribution, Variance, Probability theory, pts, probability density function, Mew* 8L liloj‘W‘Wr

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