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
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
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
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,
550.420
Introduction to Probability
Spring 2012
Midterm Examination # 4
Wednesday May 2, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistan
550.420
Introduction to Probability
Spring 2012
Final Examination
9 12 AM Monday May 14, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistan
550.420
Introduction to Probability
Spring 2012
Midterm Examination # 2
Wednesday March 7, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assist
550.420
Introduction to Probability
Spring 2012
Midterm Examination # 3
Friday March 30, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistan
550.420
Introduction to Probability
Exploration on innitely often and ultimately
Let A1 , A2 , A3 , . . . be an innite sequence of events in a probability space (, F , P ). Dene the sets
lim sup An =
Homework 9
553.420/620 Introduction to Probability
Fall 2017
Due Thursday, November 2, 2017
[1] Suppose that the time in hours required to repair a washing machine is an exponentially-distributed
rand
Homework 7
553.420/620 Introduction to Probability
Fall 2017
Due Thursday, October 19, 2017
[1] Five women and five men are ranked according to their scores on an examination. Assume that no two
score
Homework 8
553.420/620 Introduction to Probability
Fall 2017
Due Thursday, October 26, 2017
[1] A filling station is supplied with gasoline once per week. If its weekly volume of sales in tens of thou
550.420
Introduction to Probability
Fall 2012
Midterm Examination # 2
Monday November 5, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistan
550.420
Introduction to Probability
Fall 2012
Final Examination
9 12 AM Monday December 17, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assis
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, 1
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
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
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. Wha
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 fun
550.420
Introduction to Probability
Fall 2013
Midterm Examination # 3
Monday December 4, 2013
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistan
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 assistan
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 assi
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 assistanc
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 assis
550.420
Introduction to Probability
Fall 2012
Midterm Examination # 1
Friday October 5, 2012
=
NAME (Please print clearly):
SECTION:
I agree to complete this examination without unauthorized assistanc
Def (Ramsey) R(k,l) is the smallest integer n such that in any two coloring of edges of a complete
graph on n vertices by rand and blue either there is a red Kk or a blue Kl, where Kn is the n
complet
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
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),
w
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. Wha
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