550.420
Introduction to Probability
Spring 2011
First Midterm Examination
Friday April 1
NAME (Please Print Clearly)_SECTION_
I agree to complete this exam without unauthorized assistance from any person,
materials or device.
Signed _
Date _
Instructions
550.420 Introduction to Probability
Fall 2011
Homework 1
Due Thursday September 8
1. (2 points) A salad bar has 3 choices of greens, 5 veggies, 4 fruits, 3 dairy items, and 4
dressings. In how many ways can I make myself a salad with at least two of the g
550.420 Introduction to Probability
Fall 2011
Homework 2
Due Thursday September 15
1. (2 points) Let E , F , and G be three events. Determine which of the following statements are
correct and which are incorrect. Justify your answers.
(a) (E EF ) F = E F.
550.420
Introduction to Probability
Fall 2010
Second Midterm Examination
Friday October 8
NAME (Please Print Clearly)_Section # _
I agree to complete this exam without unauthorized assistance from any person,
materials or device.
Signed _
Date _
Instructi
550.420
Introduction to Probability
Fall 2011
Midterm Examination # 2
Friday October 28, 2011
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature:
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I
550.420
Introduction to Probability
Fall 2010
Third Midterm Examination
Friday November 1
NAME (Please Print Clearly)_Section # _
I agree to complete this exam without unauthorized assistance from any person,
materials or device.
Signed _
Date _
Instructi
550.420
Introduction to Probability
Fall 2011
Midterm Examination # 3
Friday December 2, 2011
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature:
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I
550.420
Introduction to Probability
Spring 2011
Midterm Examination # 3
Wednesday, May 4, 2011
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature:
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550.420
Introduction to Probability
Fall 2010
Fourth Midterm Examination
Wednesday, December 1, 2010
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signatu
550.420
Introduction to Probability
Fall 2011
Optional Final Examination
Monday, December 12, 2011
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NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature
550.420
Introduction to Probability
Spring 2011
Optional Final Examination
Monday, May 16, 2011
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature:
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550.420
Introduction to Probability
Fall 2010
Final Examination
Monday, December 13, 2010
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature:
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Instr
550.420
Introduction to Probability
Exercises on Joint Distributions
[1] Suppose X and Y are independent, X is Uniform(0,1), and Y has density f and distribution function
F . Show that the density function of X + Y is F (x)F (x1).
[2] Suppose X and Y are
550.420
Introduction to Probability
Spring 2012
Midterm Examination # 1
Friday February 17, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials or device.
Signature:
550.420
Introduction to Probability
Spring 2011
First Midterm Examination
Friday February 25
NAME (Please Print Clearly)_
I agree to complete this exam without unauthorized assistance from any person,
materials or device.
Signed _
Date _
Instructions
This
550.420
Introduction to Probability
Fall 2010
First Midterm Examination
Friday September 17
NAME (Please Print Clearly)_
I agree to complete this exam without unauthorized assistance from any person,
materials or device.
Signed _
Date _
Instructions
This
550.420 Introduction to Probability
Fall 2011
Homework 3
Due Thursday September 22
1. (2 points) Clint Westwood has collected six old guns. The probability of hitting the
bulls-eye on a target when these guns are properly aimed and fired is 0.6, 0.5, 0.7,
550.420 Introduction to Probability
Fall 2011
Homework 4
Due Thursday September 29
[1] (2 points) Two fair dice are tossed 6 times, independently. What is the probability
that the 6th sum is not a repetition of a previous sum?
[2] (2 points) Suppose that
550.420 Introduction to Probability
Fall 2011
Homework 5
Due Thursday October 6
[1] (2 points) For each of the following, determine the value(s) of k for which p(.) is a
probability frequency function. Note that in part (d), n is a positive integer.
(a) p
550.420 Introduction to Probability
Fall 2011
Homework 7
Due October 13
[1] (2 points) Before having any children, a woman and her husband want to decide in advance how many
children they will have. They want to have at least a 95% chance of having at lea
550.420 Introduction to Probability
Fall 2011
Homework 7
Due Thursday October 20
1. (2 points) Let X be a standard Cauchy random variable. Show that E [|X | ] exists if 0 < < 1
and does not exist if 1.
2. (2 points) A farmer Phil Dert who has two boards o
550.420 Introduction to Probability
Fall 2011
Homework 8
Due Thursday October 27, 2011
1. (2 points) Suppose X and Y have joint density
1
fX,Y (x, y ) = ey I(0,) (y )I(y,y) (x)
2
Compute P [X 1, Y 3].
2. (2 points) Let X have an exponential distribution w
550.420 Introduction to Probability
Fall 2011
Homework 9
Due Thursday November 3, 2011
1. (2 points) Suppose X and Y have joint density
1
fX,Y (x, y ) = ey I(0,) (y )I(y,y) (x).
2
Compute P [X 1|Y = 3].
2. (2 points) Suppose X and Y have joint density
1
f
550.420 Introduction to Probability
Homework 11
Due November 17, 2011
1. (2 points) Suppose that there are 25 students in a probability class. What
is the expected number of birthdays that belong to only one student?
2. (2 points) Thieves stole four anima
550.420 Introduction to Probability
Fall 2011
Homework 12: Extra Credit Only
Due November 21, 2011
(Monday before Thanksgiving)
In honor of the flu season, consider the following problem dealing with a simplistic
model for the spread of an epidemic.
Consi
550.420
Introduction to Probability
Fall 2011
First Midterm Examination
Friday September 30, 2011
NAME (Please Print Clearly)_
I agree to complete this exam without unauthorized assistance from any person,
materials or device.
Signed _
Date _
Instructions
6 - PROBABILITY GENERATING FUNCTIONS
Certain derivations presented in this course have been somewhat heavy on algebra. For example, determining the expectation of the Binomial distribution (page 5.1) turned out to be fairly tiresome. Another example of ha