The Central Limit Theorem
More of Probabilitys Greatest Hits!
Math 37500: Elements of Probability Theory
Volume 8 : Limit Theorems
Eli Amzallag
City College
1 / 70
The Central Limit Theorem
More of Probabilitys Greatest Hits!
Outline
1
The Central Limit T

Math 375
Name:
The following problems have been excerpted from and/or inspired by
A First Course in Probability by Sheldon Ross, 8th Edition,
Introduction to Probability by Bertsekas and Tsitsiklis,
and Probability and Statistics by Ronald Rothenberg, unl

Homework 4
Problem 1: Let be the collection of all real numbers. Fix any real number .
Define P as follows: given an event E,
1 if E
P (E) =
0 if 6 E
For example, P1 (0, ) = 1, while P1 (2, ) = 0, and for example, P (1, 1) = 0, while P (4, 4) = 1.
In this

Math 375
Name:
The following problems have been excerpted from and/or inspired by
A First Course in Probability by Sheldon Ross, 8th Edition,
Introduction to Probability by Bertsekas and Tsitsiklis,
and Probability and Statistics by Ronald Rothenberg, unl

Homework 4
Problem 1: Let be the collection of all real numbers. Fix any real number .
Define P as follows: given an event E,
1 if E
P (E) =
0 if 6 E
For example, P1 (0, ) = 1, while P1 (2, ) = 0, and for example, P (1, 1) = 0, while P (4, 4) = 1.
In this

Math 375
Name:
The following problems have been excerpted from and/or inspired by Chapter 4 of
A First Course in Probability by Sheldon Ross, 8th Edition and
A First Course in Probability and Statistics by Peggy Tang Strait, 2nd Edition,
unless otherwise

Math 375 Assignment
Try to Finish it for Sunday, February 14 (the solution will be posted on Blackboard
on Monday)
Force yourself to write and explain your reasoning clearly. As always, clarity of exposition will be a significant fraction of the grade (th

Computations involving joint pmfs and pdfs
5. Suppose we have the joint density of X and Y given by f (x, y) =
(1/2)x2 y + (1/3)y, 0 < x < 2, 0 < y < 1 and f (x, y) = 0 elsewhere.
(10 points each)
(a) Determine the probability P (0 < X < 1, 0 < Y < 1).
(b

Math 375
Name:
The following problems have been excerpted from and/or inspired by
A First Course in Probability by Sheldon Ross, 8th Edition,
A First Course in Probability and Statistics by Peggy Tang Strait,
and Probability and Statistics by Ronald Rothe

Math 375
Name:
The following problems have been excerpted from and/or inspired by
A First Course in Probability and Statistics by Peggy Tang Strait,
and Probability and Statistics by Ronald Rothenberg, unless otherwise noted.
Extra Credit : Fun with Covar

Math 375 Assignment #1: Solutions of the Sausage Problem
John has four children and four (indistinguishable) sausages. How many ways can he distribute the
sausages to the four children?
1. Answer the question by enumerating the possibilities (you dont hav

Math 375 Review Lesson (Class of February 9th)
Correction of Problem 10
(a) 8! (basic permutation).
(b) 7.2.6!
Stage 1: How many arrangements for persons A and B? 7 (1st and 2nd seats; 2nd and 3rd seats etc.).
Stage 2: For each arrangement of persons A an

Random Variables
Probability Functions
Several Important Discrete Distributions
Expectation and Variance
Cumulative Distribution Functions
Math 37500: Elements of Probability Theory
Volume 4 : Discrete Random Variables
Eli Amzallag
City College
1 / 87
Ran

MATH 375
ELEMENTS OF PROBABILITY THEORY
FALL 2015
Section: R
Schedule: Tuesdays and Thursdays from 4:00-5:40 in NAC/1511E
Instructor: Mr. Luke Rawlings
Email: lukebrawlings@gmail.com
Office: A number of different places on campus
Office hours: Thursdays a

Fundamental Counting Principle
Permutations & Combinations
Applications of Permutations and Combinations
Multinomial Coefficients
Tree Diagrams for Counting
Math 37500: Elements of Probability Theory
Volume 2 : Counting
Eli Amzallag
City College
1 / 66
Fu

What is Probability? : Four Points of View
Elements of Probability Theory
Probability Basics
Math 37500: Elements of Probability Theory
Volume 1 : Probability Basics
Eli Amzallag
City College
1 / 66
What is Probability? : Four Points of View
Elements of P

The Normal Distribution
Distribution of a Function of a Random Variable
Conditional Densities
Chebyshevs Inequality and Moment Generating Functions
Math 37500: Elements of Probability Theory
Volume 6 :
The Normal Distribution, Conditional Distributions, a

Continuous Random Variables
Expectation and Variance in the Continuous Case
Cumulative Distribution Functions of Continuous RVs
Several Important Continuous Distributions
Math 37500: Elements of Probability Theory
Volume 5 : Continuous Random Variables
El

Expectation and Variance Calculations
Poisson Processes Proofs
Math 37500: Elements of Probability Theory
Volume 5a :
Random Variables Addendum
Eli Amzallag
City College
1 / 31
Expectation and Variance Calculations
Poisson Processes Proofs
Outline
1
Expec

Conditional Probability
Bayes Theorem and Conditioning
Independence
Math 37500: Elements of Probability Theory
Volume 3 : Conditional Probability and Independence
Eli Amzallag
City College
1 / 42
Conditional Probability
Bayes Theorem and Conditioning
Inde

Joint Probability Functions
Functions of Random Variables, Expectation, and MGFs
Math 37500: Elements of Probability Theory
Volume 7 : Multiple Random Variables
Eli Amzallag
City College
1 / 88
Joint Probability Functions
Functions of Random Variables, Ex

MATH 375 ELEMENTARY PROBABILITY THEORY PROBLEM SET 1
1.
Let A = cfw_1, 3, 4, 5, 7, 9, 12, 13, 14, 19, 20 and let B = cfw_2, 3, 4, 5, 6, 7, 8, 9.
(a) Find A B.
(b) Find AB.
(c) Depict A and B by a Venn diagram. Imagine U, the universal set, is the set of a

MATH 375
The Counting Principle
1. A deli has a lunch special which consists of a sandwich, soup, dessert, and drink, all
for $4.99. The deli offers the following choices:
SANDWICH: chicken salad, ham, tuna, roast beef
SOUP: tomato, chicken noodle, vegeta