MATH11400
Statistics 1
2008-09
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
Problem Sheet 9
Remember: when online, you can access the Statistics 1 data sets from an R console by typing
load(url("http:/www.maths.bris.ac.uk/maejc/stats1/stats
Statistics 1 examination 2011 feedback on performance
Common errors, misunderstandings or other areas requiring improvement
Very few students bothered to explain their working at all (although this was not very heavily
penalised in marking); many have ver
UNIVERSITY OF BRISTOL
Examination for the Degrees of B.Sc. and M.Sci. (Level 1)
STATISTICS 1
MATH 11400
(Paper Code MATH-11400)
May/June 2011, 1 hour 30 minutes
This paper contains two sections, Section A and Section B.
Answer each section in a separate a
Mathematics Examination Feedback Form
This form is intended to provide generic feedback to students on examination
performance in individual units, in line with university code of practice for the
assessment of taught programmes. Its purpose is to help st
EXAMINATION SOLUTIONS
STATISTICS 1
MATH 11400
(Paper Code MATH-11400)
May/June 2013, 1 hour 30 minutes
Any general comments on the examination should be written here.
A1 (Ideas themselves are standard, dataset is unseen).
Creating a R vector lebron = c(20
Mathematics Examination Feedback Form
This form is intended to provide generic feedback to students on examination
performance in individual units, in line with university code of practice for the
assessment of taught programmes. Its purpose is to help st
UNIVERSITY OF BRISTOL
Examination for the Degrees of BBC. and M.Sci. (Level 0/4)
STATISTICS 1
MATH 11400
{Paper Code MATH-11400)
May/June 2013, 1 hour 30 minutes
This paper contains two sections, Section A and Section B.
Answer each section in a separate
EXAMINATION SOLUTIONS
STATISTICS 1
MATH 11400
(Paper Code MATH-11400)
May/June 2012, 1 hour 30 minutes
Any general comments on the examination should be written here.
A1 (Ideas themselves are standard, dataset is unseen).
(a) (2 marks) The median is the m
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
2.9 Assessing Fit
Say we have
a data set of n values x1 , . . . , xn
assumed to be a random sample from a population whose distribution function and pdf have the
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
Hypothesis Tests for a population mean
8.1 Introduction
A hypothesis test is a procedure for evaluating the sample evidence for or against two contrasting
statement
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
Likelihood and Maximum Likelihood Estimation
3.1 Motivation
Consider a (possibly biased) coin for which P (Head) = and P (Tail) = (1 ), where is an
unknown paramet
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
4. Linear Regression
4.1 Introduction
So far our data has consisted of observations on a single variable of interest. We now look at what
happens when we have addit
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
1.1 A Framework for Statistical Problems
Many statistical problems can be described by a simple framework in which we have:
a population of objects
a real-valued
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
2.1 Parametric Models
Parametric Family
When X is a continuous variable and the population size is large, there may be a probability density
function fX (x) which g
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
5. Distribution of Estimators: Part 1 Simulation based methods
5.1 Different methods of Estimation
So far we have seen three methods of estimating a population quan
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
Sampling distributions related to the Normal distribution
6.1 Revision of Moment Generating functions
(i) Denition
The for a continuous random variable X the moment
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
Comparison of population means
9.1 Introduction
In previous sections we have concentrated on cases where the data could be modelled as a single
random sample from a
MATH11340
Statistics 1
2004-05
Homepage http:/www.maths.bris.ac.uk/maejc/stats1/intro.html
Condence Intervals
7.1 Introduction N (, 2 ) Condence Interval for when 2 is known
Say we have a simple randon sample of size n from a Normal distribution where the