Cumulative distribution
function
Solutions to Quiz 1
and Quiz 2 Fall
2009
Why n people can be arranged in n chairs in a circle in (n-1)! ways?
The total number of arrangements to make three people, say, 1, 2, and 3 to sit
in a circle are (3-1)!
= 2! = 2. These two arrangements, are seen by taking one arrangement from each
row in the attached
figure. Please note that all the remaining
arrangements in the same row are considered equal because
they can be obtained from the preceding arrangement by going one step in
the clockwise direction.
In general, for each of the n! arrangements on a straight line, n clockwise
rotations on the circle
are lost in the ratio giving n!/n = 1.(n-1)! = (n-1)! arrangements of n people
on n chair in a circle.
Solution to sum of two independent Gammas (X, Y) with parameters (5,
λ) and (3, λ), respectively.
To see the full c.d.f. of Gamma (8, λ) see this note.
Page 1, Page 2.
Negative Binomial
Problem
Practice Problems:
Solution to Quiz 2.
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Exam I:
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Fall 2009 Exam I
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Fall 2007 Exam I Solution
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Solution to fall 2006
Exam I
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Fall 1999 p1
solution to
Fall 1999 exam I
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Exam I Spring 1996 p1
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Exam II:
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Fall 2009 Exam
II
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Fall 2007 Exam II Solution p1
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Solution Fall 2006 p1
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Math 244-002 p1
p5.
Solution to Math 244-002 p1
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Fall 1999 p1
p4.
Solution to Fall 1999 p1
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Fall 1996 p1
p4.
Solution to Fall 1996 p1
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Spring 1993 p1
p4.
Solution to Spring 1993 p1
p3
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Final Exam:
Fall 2011 Final Exam
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Fall 2010 Final Exam
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Fall 2009 Final
Exam
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Fall 2007 Final Exam
Fall 2007 Solution p1
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Fall 2006 Final Exam
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Math 244-002
p5.
Solution to Math 244-002
p5.