MATH1056: Probability and Time Series
1
Consolidation of MATH1055
1.1
Random Variables
1.2
Discrete Distributions
1.3
Continuous Distributions
1.4
Central Limit Theorem
2
Joint Probability Distributions
2.1
Joint probability density funtions
2.2
Joint cumulative distribution functions
2.3
Independence
2.4
Three or more random variables
3
Expectation, Covariance and Correlation
3.1
Expectation
3.2
Covariance
3.3
Correlation
4
Conditional distributions
4.1
Conditional Probabilities and Discrete Conditional Distributions
4.2
Continuous Conditional Distributions
4.3
Independence
4.4
Conditional Expectation
4.5
Conditional Variance
5
Transforms
5.1
One-dimensional Transformations
5.2
Two-dimensional Transformations
5.3
Maximum and Minimums
6
Multivariate Normal Distributions
6.1
Definition of Multivariate Normal Distribution
6.2
Properties of Multivariate Normal Distribution
7
A Look Ahead
8
Stochastic Process and Markov Chains
8.1
Strochastic Processes
8.2
Defintion of Markov Chains
8.3
Transition Matrix
8.4
Hitting Probabilities
9
States and Chains
9.1
Classification of States and Chains
9.2
Recurrence
9.3
Mean Recurrence Times
9.4
Periodicity
10
Equilibrium Distributions
10.1
Definition of Equilibrium Distributions
10.2
Finding Equilibrium Distributions
10.3
Limiting Behaviour
11
Renewal Processes
11.1
Definition of Renewal Processes
11.2
Renewal Processes from Markov Chains
12
Branching Processes
12.1
Discrete-Time Branching Processes
12.2
Family Sizes
12.3
Total Progey
12.4
Extinction
Probability Methods and Time Series
Chapter 7
A Look Ahead