Strand 1 Review
_ 1. Which statement describes the motion of Earth around the sun?
a. The speed of Earth is constant regardless of its distance from the sun.
b. The speed of Earth is constant because the distance remains the same
between Earth and the sun
MTH5112 Linear Algebra I 200122013
Coursework 11
Please do not submit solutions to this nal coursework, as it is not assessed and will not be marked.
Solutions will be available from the course web site.
Exercise 1. Let A Rmn .
(a) Show that N (AT A) = N
MTH5112 Linear Algebra I 200122013
Coursework 10
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MTH5112 Linear Algebra I 20122013
Coursework 8
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MTH5112 Linear Algebra I 20122013
Coursework 9
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MTH5112 Linear Algebra I 20122013
Coursework 7
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MTH5112 Linear Algebra I 20122013
Coursework 5
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MTH5112 Linear Algebra I 20122013
Coursework 6
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Coursework 4
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MTH5112 Linear Algebra I 2012-2013
Coursework 2
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Coursework 3
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MTH5112 Linear Algebra I 20122013
Coursework 1
Please hand in your solution of the starred exercise by noon on Friday 5 October using the red
Linear Algebra I Collection Box in the basement.
Dont forget to put your name and student number on your solution
4
4.1
Interval Estimation
Condence intervals
Point estimates are useful when we need a single answer, for example, to plug into some
other technique or to make a nal decision. However, a point estimate, , of will almost
always be wrong, since = with proba
5
5.1
Hypothesis Testing
Denitions
We assume that Y1 , . . . , Yn have a joint distribution which depends on the unknown parameters 1 , . . . , p . The set of all possible values of is called the parameter space .
A hypothesis restricts to lie in , where
2
2.1
Point Estimation
Denitions
We have the following probability model for the population from which the data y1 , y2 , . . . , yn
are a sample: Y1 , Y2 , . . . , Yn have a joint distribution which is specied, except for the unknown parameters 1 , 2 , .
B. Sc. Examination by course unit 2013
MTH 6136
Statistical Theory
Duration: 2 hours
Date and time: 30 May 2013, 10.00-12.00
Apart from this page, you are not permitted to read the contents of
this question paper until instructed to do so by an invigilato
3
3.1
Methods of Estimation
Method of moments
The kth population moment about the origin of a random variable Y is
k = E(Y k ),
k = 1, 2, . . . ,
and the kth sample moment about the origin of a random sample Y1 , . . . , Yn is
1 n k
mk =
Y ,
n i=1 i
k = 1