(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 11
This lecture
10. Brownian Motion and Stationary Processes
10.1 Brownian Motion
10.2 Hitting times and Maximum Variable
10.3 Variations on Brownian Motion
10.5 White
Homework 6 (Stats 620, Winter 2017)
Due Thursday March 16, in class
1. In a branching process the number of offspring per individual has a Binomial (2, p) distribution. Starting with a single individual, calculate:
(a) the extinction probability;
(b) the
Math 310-2
Homework 6 Solutions
TA in charge: Honghao Gao. Accuracy: 1,5,7,8
1. Suppose the transition function P of a branching chain satisfies P (1, 1) < 1. Show that every
state other than 0 is transient.
Proof. Two cases. (1) If P (1, 0) > 0, then for
Conditionally accept
offer
OR
Conditionally defer
offer
OR
Conditionally reject
offer
Check for an offer in
the next offer round
Check for an offer
in the next offer
round
Check for an offer
in the next offer
round
If you receive
another offer for the
sam
(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 3
This lecture
2. Random Variables
2.6 Moment Generating Functions
2.8 Limit Theorems
3. Conditional Probability and Conditional Expectation
3.1 Introduction
3.2 The Di
(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 2
This lecture
2. Random variables
2.4 Expectation of a Random Variable
2.5 Jointly distributed Random Variables
2.6 Moment Generating Functions
Stochastic Processes (M
(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 7
This lecture
5. The Exponential Distribution and the Poisson Process
5.2 The Exponential Distribution
5.3 The Poisson Process
Stochastic Processes (MATH3801-3901)
Dr
(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 8
This lecture
5. The Exponential Distribution and the Poisson Process
5.3 The Poisson Process
5.4 Generalisations of the Poisson Process
6. Continuous-Time Markov Chai
(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 1
This lecture
1
Introduction to Probability Theory
1.1 Introduction
1.2 Sample Space and Events
1.3 Probabilities
1.4 Conditional Probabilities
1.5 Independent Events
(Higher) Probability and Stochastic Processes
MATH3801-MATH3901
Session 1, 2013 - Week 9
This lecture
6. Continuous-Time Markov Chains
6.1 Introduction
6.2 Continuous-time Markov Chains
6.3 Birth and Death Processes
6.4 The Transition Probability Function
Chapter 2
Unbiased Estimation
If the average estimate of several random samples is equal to the population parameter
then the estimate is unbiased. For example, if credit card holders in a city were
repetitively random sampled and questioned what their ac