Homework2

# Homework2 - STAT 380, Fall 2010 HW 2Solutions (Chapters 3 &...

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STAT 380, Fall 2010 HW 2Solutions (Chapters 3 & 4) 1. Let X be a continuous r.v. with probability density function given by f(x) = 200 10 x for 10 x c 0 Otherwise a. Determine c such that f(x) is a probability density function. Using 10 10 1 200 c x dx , we get c=30, -10. But the lower bound of the interval is 10, so c cannot be negative. So, c=30. b. Find P(15<X<20). 20 15 10 0.1875 200 x dx c. Find E(X). 30 10 10 70 / 3 23.33 200 x xd x  d. Find s.d(X). Var(X)=E(X 2 )-{E(X)} 2 = 30 22 10 10 (70 / 3) 200 / 9 200 x x  s.d.(X)= 200 / 9 =4.714 e. Find the cdf of X. F(x)= 0 if x<10 2 20 100 400 xx  if 10 x 30 1 if x>30

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2. Roll a pair of dice. Let X = no. on die 1 and Y =no. on die 2. 1 for x and y=1,2,3,4,5,6 f(x,y) 36 0 otherwise a.Find the marginals of X and Y. 6 1 36 1 6 36 1 ) , ( ) ( 6 1 6 1 y y y x f x g , x=1,2,3,4,5,6. 6 1 36 1 6 36 1 ) , ( ) ( 6 1 6 1 x x y x f y h , y=1,2,3,4,5,6. b. Are X and Y independent?
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## This note was uploaded on 01/25/2011 for the course MATH 380 taught by Professor Staff during the Fall '08 term at UNL.

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Homework2 - STAT 380, Fall 2010 HW 2Solutions (Chapters 3 &...

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