600.465 Natural Language Processing
Assignment 2: Probability Exercises
Prof. J. Eisner Fall 2012
Due date: Wednesday 26 September, 2 pm
No programming is required for this assignment.
How to hand in your work: Put all notes, documentation, and answers to
550.420
Introduction to Probability
Exercises on Combinatorics
[1] A salad bar has 3 choices of greens, 8 veggies, 5 fruits, 3 dairy items, and 4 dressings. In how many
ways can I serve myself a salad with at least one of the greens, either 3 or 4 veggies
550.420 Introduction to Probability - Fall 2105
Homework #02
Due at the beginning of lecture, Friday, September 18.
Do the following exercises from the course textbook:
Chapter 1: 19, 21, 22, 23, 27, 30.
Do the following additional problems:
A.2.1. Suppos
550.420
Introduction to Probability
Fall 2012
Midterm Examination # 2
Monday November 5, 2012
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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:
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550.420
Introduction to Probability
Spring 2012
Midterm Examination # 4
Wednesday May 2, 2012
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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:
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550.420
Introduction to Probability
Spring 2012
Final Examination
9 12 AM Monday May 14, 2012
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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:
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I
550.420
Introduction to Probability
Spring 2012
Midterm Examination # 2
Wednesday March 7, 2012
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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:
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550.420
Introduction to Probability
Spring 2012
Midterm Examination # 3
Friday March 30, 2012
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I
Probability Model
o
Random Experiment
n
o
A situation where the outcome is not predictable
with certainty in advance.
Probability Model (for a random experiment)
n
n
n
S = sample space
F = sigma-field
P = probability function
One Sentence Descriptions
o
o
550.420
Introduction to Probability
Exploration on the Rayleigh Distribution
The Rayleigh distribution is a continuous distribution with cumulative distribution function
x2
F (x) = 1 e 22 I[0,) (x),
where the parameter > 0.
A general class of applications
550.420
Introduction to Probability
Exploration on Pigeonhole Principle
The pigeonhole principle is the fact that if you distribute more than n items into n pigeonholes, then at
least one pigeonhole will contain more than one item.
A very simple example i
550.420
Introduction to Probability
Fall 2012
Final Examination
9 12 AM Monday December 17, 2012
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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
Fall 2012
Midterm Examination # 1
Friday October 5, 2012
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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:
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I
550.420 Introduction to Probability - Fall 2105
Homework #01
Due at the beginning of lecture, Friday, September 11.
Do the following exercises from the course textbook:
Chapter 1: 1, 2, 5, 6, 7, 9a, 10, 14, 16, 17, 18.
Do the following additional problems
EN.550.420 Homework 1
Lue Xu Sep.4.2015
Chapter 1
1.
c
c
c
c
A= cfw_2,4,6 , B= cfw_ 4,5,6 . A B= cfw_ 2,4,5,6 , A B= cfw_ 6 . A =cfw_ 1,3,5 , B = cfw_1,2,3 .( A B) = cfw_1,3 ,( A B) =cfw_1
.
A c Bc = cfw_1,3 =( A B )c , A c Bc = cfw_1,2,3,4,5 =( A
Syllabus
Applied Mathematics and Statistics 550.420
Introduction to Probability
Fall 2015
(4 credits, EQ)
Description
Probability and its applications, at the calculus level. Emphasis on techniques of application rather than on
rigorous mathematical demon
550.420
Introduction to Probability
Exercises on Discrete Random Variables
[1] A fair die is rolled six times independently. If the outcome is k on the k-th roll, we say that a match
has occurred. What is the probability that at least one match occurs?
[2
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
Fall 2013
Midterm Examination # 3
Monday December 4, 2013
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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
Fall 2013
Midterm Examination # 2
Monday November 4, 2013
=
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
Fall 2013
Final Examination
2 5 PM Thursday December 19, 2013
=
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 2013
Midterm Examination # 2
Monday April 1, 2013
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistance from any person, materials, or device.
Signature:
=
I
550.420
Introduction to Probability
Fall 2012
Midterm Examination # 3
Wednesday December 5, 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
Exploration on Simpsons Paradox
Two hospitals, A and B, are comparing their recovery rates. Both hospitals treat three types of patients:
minor illnesses, severe illnesses, and life-threatening illnesses. For each type
550.420
Introduction to Probability
Exploration on Pinochle
The card game of Pinochle is played with an unusual deck of 48 playing cards, which has the usual four
suits (Clubs, Diamonds, Hearts, and Spades), but with each suit containing two of each of th
550.420
Introduction to Probability
Exercises on Conditional Probability
[1] In a small lake, it is estimated that there are 105 sh, of which 40 are trout and 65 are carp. A sherman
caught 8 sh. What is the probability that exactly two of them are trout i
550.420
Introduction to Probability
Exercises on Probability Measure
1
[1] Consider a room containing N unrelated people, each with probability 12 of being born in each month
1
of the year. For which values of N is the probability greater than 2 that ther
Natural Language Processing (600.465)
Jason Eisner ([email protected] / Hackerman 324C)
First-Day Questionnaire - Sep. 5, 2012
Name (include nickname):
Email (important! be legible!):
Major, year, etc.:
Are you in this class for credit, for audit, or
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