ST202 Stochastic Processes, Term 1 2013: Hand-out 8
K. Latuszynski
The simple symmetric random walk in Z3
The statement of the following theorem is examinable but its proof is not. The proof is a version of the one
appearing in the book Markov chains by J
ST202 Stochastic Processes, Term 1 2013: Hand-out 4
K. Latuszynski
A crash course in generating functions
This sheet is based on notes written by Prof. Wilfrid Kendall and aims to remind you
of some material from ST112 Probability B. Any errors, however,
ST202 Stochastic Processes, Term 1 2013: Hand-out 7
K. Latuszynski
More branching process examples
This hand-out gives more examples of applications of the theory of branching processes
that we developed in lectures. This sheet is based on notes written b
ST202 Stochastic Processes, Term 1 2013: Hand-out 3
K. Latuszynski
Periodicity
This sheet gives the proof of a result stated in lectures and is based on notes written by
Prof. Wilfrid Kendall. Please send comments and corrections to
K.G.Latuszynski@warwic
ST202 Stochastic Processes, Term 1 2013: Hand-out 6
K. Latuszynski
The Hardy-Weinberg law
This sheet is based on notes written by Prof. Wilfrid Kendall. Any errors, however, are my
responsibility. Please send comments and corrections to K.G.Latuszynski@wa
ST202 Stochastic Processes, Term 1 2013: Hand-out 9
K. Latuszynski
Coupling and the renewal theorem
This hand-out gives a proof of the renewal theorem via a very beautiful method called
coupling. The elementary renewal theorem and the renewal theorem form
ST202 Stochastic Processes, Term 1 2013: Hand-out 2
K. Latuszynski
Variant forms of the Markov property
This sheet is intended to give all the details of some straightforward (but messy!) calculations and is
based on notes by Dr Christina Goldschmidt, alt
ST202 Stochastic Processes, Term 1 2012: Hand-out 1
K. Latuszynski
First year probability
This sheet provides a very brief summary of some of the material covered in ST111/ST112 Probability
A and B. You are expected to be well-versed in all of the materia
ST202 Stochastic Processes, Term 1 2013: Hand-out 5
K. Latuszynski
Example: Asymmetric random walk with one
absorbing barrier at 0
Please send comments and any corrections to K.G.Latuszynski@warwick.ac.uk.
Recall from the lectures the following facts that
Introduction
The firm named Fast Track Couriers has been in to the market since long and is a courier
organization that has always been operating within New South Wales for last 15 years.
The primary business of the firm is all related to delivering the m
1.09 Selecciones- El Viaje por el Golfo de Mxico
Prctica
Answer the following questions in complete sentences in Spanish. To answer these
questions, you will need to refer back to the reading in the lesson. Your responses here
will be submitted for gradin
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 3 (Week 4)
Example 1: Balanced Incomplete Blocks (Lecture 7)
Construct a BIB for 16 treatments in 20 blocks of four by starting with a set of three mutually
orthogonal Latin Squares.
Three mut
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 6 (Week 7)
Exercise 1: Multiple Regression (Lecture 14)
The following data show the responses (%age of total calories obtained from complex
carbohydrates) for 20 male, insulin-dependent diabet
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Worksheet 1 (Week 2)
Exercise 1: Motivating examples (Lectures 1, 2)
Look at the motivating examples at the beginning of Lecture 1. How might you define the
experimental unit in these experiments?
Exercise 2: Random
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 5 (Week 6)
Exercise 1: Random Effects (Lecture 11)
A textile company weaves a fabric on a large number of looms. It would like the looms to be
consistent so that it obtains a fabric of uniform
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Worksheet 3 (Week 4)
Example 1: Balanced Incomplete Blocks (Lecture 7)
Construct a BIB for 16 treatments in 20 blocks of four by starting with a set of three mutually
orthogonal Latin Squares.
Three mutually orthogo
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 1 (Week 2)
Exercise 1: Motivating examples (Lectures 1, 2)
Look at the motivating examples at the beginning of Lecture 1. How might you define the
experimental unit in these experiments?
Discu
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 4 (Week 5)
Exercise 1: 4 4 Lattice square (Lecture 8)
Write out a lattice square design for 16 treatments. You will need the following orthogonal
4 4 Latin squares:
1
2
3
4
2
1
4
3
3
4
1
2
4
3
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 7 (Week 9)
Exercise 1: Confounding and fractional replication (Lectures 16/17)
Discuss briefly the situations in which fractionally replicated factorial experiments may be
useful, and explain
DESIGNED EXPERIMENTS 2016
ST305 / ST410
Solutions to Worksheet 2 (Week 3)
Exercise 1: Analysis of CRD (Lecture 3)
Consider the weights of eggs from five different breeds of hen, as follows:
breed 1
64.1
60.2
53.8
67.2
56.9
58.6
60.0
66.3
50.7
56.0
63.3
58
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 8, with solutions1
Blessed is he who has found his work;
let him ask no other blessedness
Thomas Carlyle (17951881), Past and Present.
A: warm-up questions
1. The price of a share is mo
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 7, with solutions1
Neo: I know what youre trying to do.
Morpheus: Im trying to free your mind, Neo. But I can only show you the door. Youre the one who
has to walk through it.
A: warm-u
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 6, with solutions1
A University should be a place of light, of liberty, and of learning.
Benjamin Disraeli (18041881), Speech in the House of Commons, 1873
A: warm-up questions
1.
(a) C
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 5, with solutions1
Old age is the most unexpected of things that can happen to a man
Leon Trotsky (18791940).
A: warm-up questions
1. Consider a 3 3 transition matrix
3
8
1
4
P
3
8
0 0
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 4, with solutions1
It is impossible to enjoy idling thoroughly
unless one has plenty of work to do
Jerome K. Jerome (18591927), Idle Thoughts of an Idle Fellow
A: warm-up questions
1. C
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 3, with solutions1
Happiness is when what you think, what you say,
and what you do are in harmony.
Mahatma Gandhi (1869 1948)
A: warm-up / revision questions
1. Prove the following resu
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 2, with solutions1
Genius is one per cent inspiration
and ninety-nine per cent perspiration
Thomas Alva Edison, 1847-1931, Newspaper interview.
A: warm-up questions
1. Two players A and
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 1, with solutions1
Begin at the beginning, and go on till you come to the end; then stop.
Lewis Carroll, Alice in Wonderland.
A: warm-up questions
1. Recall the Gamblers ruin example fr
ST202 Stochastic Processes, Term 1 2012
K. Latuszynski
Exercise Sheet 11
Begin at the beginning, and go on till you come to the end; then stop.
Lewis Carroll, Alice in Wonderland.
A: warm-up questions
1. Recall the Gamblers ruin example from lectures.
Sup