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Theory Of Statistics Question Paper
Theory Of Statistics
Course:Master Of Economics
Institution: Kenyatta University question papers
Exam Year:2009
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF MASTER OF
ECONOMICS
EES 502:
THEORY OF STATISTICS
DATE: Tuesday, 1st December, 2009
TIME: 9.00 a.m. – 12.00 p.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer ALL questions.
1.
a)
We select two balls at random without replacement from a basket that
contains four white and eight black balls.
i)
Compute the probability that both balls are white
(2 marks)
ii)
Compute the probability that the second ball is white
(3 marks)
b)
Prove that by Chebyshev’s inequality, if x is any random variable with the
mean E(x)= µ, a variance V (x)
2
=s and ? be a small positive deviation
V x
form the mean, then p ( x - µ = )
( )
? =
.
(10
marks)
2
?
c)
If
?=5 and 5
k = in (b) above, what is the probability of a deviation from
the mean by more than k standard deviations (5 standard deviations)?
(4 marks)
Page 1 of 2
2. Prove
that;
a)
If
E and E are subsets of S, then;
1
2
P (E ? E = P E + P E - P E n E
(12
marks)
1
2 )
( 1) ( 2) ( 1 2)
b)
if
events
E and E are subsets of S such that E is a subset of E then
1
2
1
2
p (E < p E
(10 marks)
1 )
( 2)
3.
a)
A manufacturer of metal pistons finds that on the average, 12% of his
pistons are rejected because they are either oversize or undersize. What is
the probability that a bath of 10 pistons will contain;
i)
No
more
than
2
rejects?
(5
marks)
ii)
at
least
2
rejects?
(4
marks)
b)
A company pays its employees an average wage of Kshs 3.25 an hour with
a standard deviation of 60 cents. If the wages are approximately normally
distributed, determine;
i)
The proportion of the workers getting wages between Kshs 2.75
and Kshs 3.69 an hour
(6 marks)
ii)
The minimum wage of the highest 5%
(2 marks)
4.
The following sample for the emissions of nitrogen-oxide (in grams per mile) for
eight cars was obtained: 0.07, 0.11, 0.14, 0.13, 0.08, 0.16, 0.08, 0.10. Assume
that the population form which the sample was obtained is normally distributed.
If the Environmental Protection Agency requires that the average nitrogen-oxide
emissions be less than 0.164 grams/mile, can we safely conclude at a 5% level of
significance that this requirement is being met
(12 marks)
Page 2 of 2
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