Probability I - Homework 2
Sunhwa
Sep 2015
10) There are two dice on the table. One is a fair die, the other
is xed so that it always comes up showing an even number. You
pick one die at random and ro
Probability Hw 8
Sunhwa
January 28, 2016
(1) A simplied version of the Google page-rank algorithm assigns
a probability distribution R(1), . . . , R(n) to a collection of n webpages.
The webpages are
Probability I - Homework 3
Sunhwa
2015
18) A rat is trapped in a maze with three doors. Door #1 leads
to the exit after 1 minute. Door #2 returns to the maze after three
minutes. Door #3 returns to th
Probability I - Hw 9
Sunhwa
2015
(1) Let cfw_Xt : t 0 be a CMTC on the state space = cfw_1, 2, 3 with
the following transition rates:
12 = 1, 21 = 10
23 = 1, 32 = 5
and all other rates zero.
(a) Find
Ch. 1: Elementary Probability Theory
Christopher King, Northeastern University
August 4, 2016
0.1
Basics: sample space, events, probability law
Probability theory provides the tools to organize our th
Probability I - Homework 6
Sunhwa
2015
(1) For a Markov chain, suppose that state i is transient, and state
i is accessible from state j (meaning that there is some integer m s.t.
pji (m) > 0). Show t
Probability I - Homework 1
Sunhwa
Sep
1) Given three events E, F, G, write formulas for the following
events: only E is true; both E and F but not G; at least two of
the events are true
i Let E, F, G
Probability Hw 7
Sunhwa
2015
(1) A random walk is dened on the integers cfw_ 0,1,2,3,. . . with
the following transition probabilities
1
1
p00 = , p01 =
2
2
1
pn,n+1 = pn,n1 = ; n = 1, 2, . . .
2
Det
MTH 7241: Fall 2015: Prof. C. King
Assignment 9
Due date: Thursday, December 10.
Reading: slides on Blackboard Ch. 5a: Branching Processes, Ch. 6: Continuous time
Markov chains.
Problems:
1). Let cfw_
MTH 7241: Fall 2016: Prof. C. King
Practice Problems for Test 2
1) Consider a Markov chain on a discrete state space. Suppose that state i has period 2, and that state j is
accessible from state i. Pr
MTH 7241 (Prof. King): FALL 2015: FINAL
December, 2015
You may use your notes and the texts and handouts for the course. You may not use other resources, either
online or offline. Do not discuss the p
MTH 7241: Fall 2015: Prof. C. King
Assignment 8
Due date: Tuesday, November 17.
Reading: slides on Blackboard Ch. 4: Infinite Markov chains and Ch. 5: Large
Deviations for IID sums.
Problems:
1). A si
MTH 7241: Fall 2015: Prof. C. King
Assignment 7
Due date: Tuesday, November 10.
Reading: slides on Blackboard Ch. 4: Infinite Markov chains.
Problems:
1). A random walk is defined on the integers cfw_
MTH 7241: Fall 2015: Prof. C. King
Assignment 5
Due date: Thursday, October 15.
Reading: slides on Blackboard Ch. 2: Finite Markov Chains. Also Grinstead and Snell
Chapter 11
Note: the text by Grinste
MTH 7241: Fall 2015: Prof. C. King
Assignment 6
Due date: Thursday, October 29.
Reading: slides on Blackboard Ch. 3: Infinite random sequences, and Ch. 4: Infinite
Markov chains.
Problems:
1). For a M
MTH 7241: Fall 2015: Prof. C. King
Assignment 2
Due date: Thursday, September 24.
Reading: slides on Blackboard Ch. 1: Elementary Probability Theory. If needed see
Grinstead and Snell for background m
Probability I - Homework 5
Sunhwa
January 28, 2016
(1) A transition matrix is doubly stochastic if each column sum is
1. Find the stationary distribution for a doubly stochastic chain with
M states.
L
Probability Theory: Ch 1 Problems
September 6, 2016
Exercise 1 Given three events E, F, G, write formulas for the following events: only E is true;
both E and F but not G; at least two of the events a
Engineering Probability and Statistics, IE6200
Fall 2016
Class Room: SH 315
Instructor: Professor Fard, Office: 317 SN, E-mail: [email protected]
Prerequisites: Differential and Integral Calculus
Office
Engineering Probability and
Statistics, IEM G200
By: Professor Nasser Fard
Lecture Six
12/09/16
1
Outline
Continuous Random Variables
Exponential Distribution
Gamma Distribution
Beta Distribution
12/0
Engineering Probability and
Statistics, IEM G200
By: Professor Nasser Fard
Fall 1014
Lecture
Tenth
12/09/16
1
Outline
Confidence Interval for
Confidence Interval for difference of
two means
Confid
Engineering Probability and
Statistics, IE6200
By: Professor Nasser Fard
Fall 2013
Outline
What is Probability?
Basic Concepts of Probability
Review on Set Theory
Probability Function
Probability Theo
Engineering Probability and
Statistics, IE 6200
By: Professor Nasser Fard
Lecture Ten
Outline
Maximum Likelihood Estimation
Sample Size
Test of Statistical Hypotheses
Tests about one proportion
Tests
Engineering Probability and
Statistics, IE 6200
By: Professor Nasser Fard
Lecture
Seven
12/09/16
1
Outline
Distributions of Sums of
Independent Random Variables
Central Limit Theorem
Functions of R
MTH 7241: Fall 2015: Prof. C. King
Assignment 3
Due date: Thursday, October 1.
Reading: slides on Blackboard Ch. 1: Elementary Probability Theory. If needed see
Grinstead and Snell for background mate
MTH 7241: Fall 2015: Prof. C. King
Assignment 1
Due date: Thursday, September 17.
Reading: slides on Blackboard Ch. 1: Elementary Probability Theory. If needed see Grinstead and Snell
for background m
MTH 7241: Fall 2015: Prof. C. King
Assignment 4
Due date: Thursday, October 8.
Reading: slides on Blackboard Ch. 2: Finite Markov Chains, and Grinstead and Snell.
Note: the text by Grinstead and Snell