Chapter 1: Combinatorial Analysis
Concept
Formula
Counting
Total number of outcomes
for r performed experiments,
each one resulting in ni outcomes.
Ordering
Number of different ways of ordering
r elements chosen among n elements.
Lottery
(How many sequenc
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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