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 check whether
We can try to use the ratio test to check if
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 a subset of the sample space. Solution: The sample spac
Math 425 (Fall 08)
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 4 Independents. How many committees are possible?
2 (10
Math 425 (Fall 07)
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) the role of the mean and the variance. iv) What is the
SPRING 2009
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 otherwise. (a) Are X and Y independent? (b) Find E [X ].
SPRING 2009
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 tosses of a coin, the coin lands heads 5800 times. Is it
Math 425 (Fall 07)
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 Democrats have a majority on the committee? What is the conditi
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 (x, 0) = U (x, b) = x2 . 2 Seeking U (x, y ) = X (x)Y (y