Quiz_6_solutions

Quiz_6_solutions - f) (5 points) Find the variance of Y? a)

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Quiz #6 – Friday, October 12 th NAME: ______________________________ Grade: __________ out of 25. You have 20 minutes to complete this Quiz. This Quiz is a closed book and Notes exam Exercise 1: (30 points) Let say that the probability that someone will fail X number of classes during the semester is as follows. X 0 1 2 3 4 P(X=x) 0.8 0.1 0.05 0.03 0.02 a) (5 points) Find expected value of X? b) (5 points) Find the variance of X? c) (5 points) Find the skewness of the distribution above. d) (5 points) Find the moment generating function of X e) (5 points) If the university charge your bursar account with 3 2 2 3 Y X X X = + - what is the amount that a random student will be charged at the end of the semester.
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Unformatted text preview: f) (5 points) Find the variance of Y? a) E(X)=0.8*0+1*0.1+2*0.05+3*0.03+4*0.02=0.37 b) E(X 2 )=0.8*0+0.1*1 2 +0.05*2 2 +0.03*3 2 +0.02*4 2 =0.89 Var(X)= E(X 2 )-E(X)E(X)=0.89-0. 37 2 =0.7531 c) E((X-E(X)) 3 )=0.8(0-0.37) 3 +0.1(1-0.37) 3 +0.05(2-0.37) 3 +0.03(3-0.37) 3 +0.02(4-0.37) 3 = =1.703 skewness=1.703\(0.7531) 3/2 =2.6058 d) MX(t)=0.8+0.1e 1t +0.05e 2t +0.03e 3t +0.02 e 4t e) X=0 => Y=0, X=1 => Y=0, X=2 => Y=10, X=3 =>Y=36, X=4=> Y=84 So E(Y)= 0.8*0+0*0.1+10*0.05+36*0.03+84*0.02=3.26 f) E(Y 2 )=0.8*0+0.1*0+0.05*100+0.03*1296+7056*0.02=185 So Var(Y)=185-3.26*3.66=174.37...
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