Exam Date 1 Exam Duration Session
3
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University of the Witwatersrand, Johannesburg
Course Code No(s) STATZOiZ
Course Description mamas) An introduction to Ma-thematicai Statistics
Date of Examination 1 2 November 2015
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Introduction to Mathematical Statistics
STAT2012
Dr C Chimedza
Tutorial 9
1. A random sample of 35 households was selected as part of a study on electricity usage, and
the number of kilowatt-hours was recorded for each household in the sample. The average
Introduction to Mathematical Statistics [STAT2012]
Dr C Chimedza
Tutorial 3
1) Rewrite the following sets using set notation.
(a) Natural Numbers greater than 2 but less than 10
(b) cfw_1,3,7,11,13,17,23,29
(c) (2,5) Hint: this is an interval
2) Let A=cfw
Introduction to Mathematical Statistics
STAT2012
Dr C Chimedza
Tutorial 10
1. The blood pressure (y) in mmHg and ages (x) in years of patients were recorded at a clinic. These
are shown in the table below.
Age
Blood pressure
42
98
74
135
45
121
35
90
60
1
Introduction to Mathematical Statistics [STAT2012]
Dr C Chimedza
Tutorial 7
1.
A lazy teacher randomly assigns the marks of students by picking an integer uniformly from 65
to 84 (inclusively) (assume all marks are unique).
(a) What is the probability tha
Introduction to Mathematical Statistics [STAT2012]
Dr C Chimedza
Tutorial 6
1.
2.
3.
Suppose the distribution function of X is given by
0
<0
() = cfw_1/2 0 < 1
1
1<
(a) Find E(X).
(b) Find Var(X).
If the distribution function of X is given by
0
<0
1/2 0 <
Introduction to Mathematical Statistics
STAT2012
Dr C Chimedza
Tutorial 8
1. Suppose a random variable X has an exponential distribution with mean 100,
(a) What is the probability that > 100.
(b) ( > 30)
2. A random variable X follows a normal distributio
Introduction to Mathematical Statistics [STAT2012]
Dr C Chimedza
Tutorial 4
1.
2.
3.
4.
What is the probability that a two digit number selected at random will be a multiple of '3' and not a
multiple of '10'?
A glass jar contains 6 red, 5 green, 8 blue an
Introduction to Mathematical Statistics
Dr C Chimedza
Tutorial 2
Answer all the questions.
Consider the marks obtained in a test written by STAT2012 students below:
77
30
75
70
75
90
26
32
80
90
81
62
78
64
33
75
33
76
35
75
81
36
71
42
68
77
85
36
77
65
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HOMEWORK 1
SOLUTIONS
(1) Determine all m, n N such that the complete bipartite graph Km,n is Hamiltonian.
Solution:
Claim 1. The complete bipartite graph Kn,n is Hamiltonian, for all n 2.
Proof. Kn,n is a simple graph on 2n vertices. So for n 2, we have t
Notes on Hamiltonian cycles
Definition 1. A graph G is k-connected if there does not exist a set of at most k 1 vertices of G whose
removal yield a disconnected graph.
Definition 2. An alternative definition of a path is a sequence of vertices of a graph