University of Bath, Department of Economics
ron Tth, 2012
Pre-sessional Mathematics and Statistics for MSc Students
Exam 2012 - SOLUTIONS
Time allowed: 2 hours. A calculator may be used for this Examination.
1) Consider the following matrix:
1
2
A= 0
0
A.

University of Bath, Department of Economics
ron Tth, 2013
Pre-sessional Mathematics and Statistics for MSc Students
Denitions and Some Basic Transformations
1
Expected Value
n
xi pi
E(X) =
or
xf (x)dx
i=1
Some rules:
E(X + Y ) = E(X) + E(Y )
E(bX) = bE(X)

Induction Course in Mathematics and Statistics
Handout 1: Matrix Algebra
Department of Economics
University of Bath
September 2011
1
Denitions
A matrix is a rectangular array of numbers. An n m matrix has n rows and
m columns. An element of a matrix A at

University of Bath, Department of Economics
ron Tth, 2014
Pre-sessional Mathematics and Statistics for MSc Students
Exam 2014 - SOLUTIONS
GENERAL COMMENTS:
Q1: Most of you had no trouble with this question. However, remember that when you claim
something

University of Bath, Department of Economics
ron Tth, 2013
Pre-sessional Mathematics and Statistics for MSc Students
Exam 2013 - SOLUTIONS
GENERAL COMMENTS:
Q1: Most of you had no trouble with this question. However, remember that when you claim
something

Induction Course in Mathematics and Statistics
Handout 5: Statistical Inference
Department of Economics
University of Bath
September 2011
Statistical inference is concerned with learning about the properties of population from the properties of a sample f

Induction Course in Mathematics and Statistics
Handout 4: Probability Distributions
Department of Economics
University of Bath
September 2011
1
Random variables
A random variable is a variable whose value depends on the outcome of a
random experiment. The

Induction Course in Mathematics and Statistics
Handout 3: Dynamics. Dierential Equations.
Department of Economics, University of Bath
September 2009
Denition. An equation F (x; y; y 0 ; : : : ; y (n) ) = 0 which assumes a functional relationship between i

Basic Dierential Equations
September 22, 2014
An equation F (t, y(t), y (t), ., y (n) (t) = 0, which denes a functional relationship between the
independent variable, the function y(t) and its derivatives, is called the ordinary dierential equation
(ODE)

Induction Course in Mathematics and Statistics
Handout 2: Calculus
Department of Economics
University of Bath
September 2011
1
Derivatives
dy
) which
The derivative of a function y (x) is the new function y 0 (x) (or
dx
assigns to each value of the indepe