MATH 450 Section 002 Homework 5 Solutions Winter 2009
Section 17.9, p. 919, #2. (b)
a( ) =
1
f (x) cos(x )dx =
1
L 0
L
x cos(x )dx
0
1 =
sin(x ) x
1 x=0
L
sin(x ) L sin(L ) 1 dx = +
cos(x ) 2
L x
MATH 450 Section 002 Homework 3 Solutions Winter 2009
Section 17.5, p. 880 #2(b). Since  sin(2nx) 1 sin(2nx) = 2 =: Mn , 2n + 2 n 2n + 2 (n 1)2 + 1 Mn < and try to use the Mtest.

n2
we can che
SPRING 2009
MATH 425
Ralf Spatzier
Homework 1  Solutions (1) If two balanced dice are rolled, what is the probability that the sum of spots is equal to ve? Describe the sample space and the event as
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Midterm 1
October 2, 2008
1 (10 pts) A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from a group of 5 Republicans, 6 Democrats, and
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Midterm 2
November 7, 2007
1 (10 pts) i) Give an example of a discrete random variable and one of a continuous random variable. ii) What is a random variable? iii) Describe (briey)
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MATH 425
Ralf Spatzier
Homework 5
for Wednesday, June 10
(1) The random variables X and Y have the joint density function f (x, y ) = 12x y (1 x) for ) < x < 1, 0 < y < 1 and equal to 0 ot
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MATH 425
Ralf Spatzier
Homework 4
for Friday, June 5
(1) Suppose X is a normal random variable with mean 5. If P (cfw_X > 9) = .2, approximate what is V ar(X ). (2) In 10,000 independent t
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Final Exam
December 17, 2007
1. A committee of size three is to be selected from a group of 6 Democrats, 5 Independents, and 4 Republicans. What is the probability that the Democrat
MATH 450 Section 002 Homework 7 Solutions Winter 2009
Section 20.2, p. 1067, #15. (a) Let u(x, y ) = f x2 + U (x, y ), then U (x, y ) 2 satises Uxx + Uyy = 0, f U (0, y ) = 0, U (a, y ) = a2 , 2 f U (