ECON 250 Final: ECON 250 Pastfinals Econ250fxW10 corrected
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QUEEN’S UNIVERSITY
FACULTY OF ARTS AND SCIENCE
APRIL 2010
ECONOMICS 250
Introduction to Statistics
Instructor: Gregor Smith
Tutors: Michael Haymes, Jier Pan
Instructions:
The exam is three hours in length.
Do all nine (9) questions.
Be sure to show your calculations and intermediate steps.
Put your student number on each answer booklet.
Formulas and tables are printed at the end of this question paper.
You may use a hand calculator. Allowed calculators include those with blue or gold
stickers, the Casio 991, the Sharp EL376S, or other non-programmable calculators. No
red-sticker calculators or other aids are allowed.
Proctors are unable to respond to queries about the interpretation of exam questions.
Do your best to answer the exam questions as they are written.
This material is copyrighted and is for the sole use of students registered in Economics
250 and writing this exam. This material shall not be distributed or disseminated.
Failure to abide by these conditions is a breach of copyright and may also constitute a
breach of academic integrity under the University Senate’s Academic Integrity Policy
Statement.
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1. A random variable Xcan take on the values 1, 2, 3, 4, or 5 in its population, each
with the same probability.
(a) Find the mean and variance of X.
(b) A second variable is given by Y=10 −2X. Find the mean and variance of Y.
(c) What is the correlation coefficient between Xand Y?
2. The probability of being unemployed conditional on being a university graduate
is 0.05. The probability of being unemployed conditional on being a non-graduate is
0.15. The probability of anyone graduating from university is 0.45.
(a) What is the probability of being a university graduate and being unemployed?
(b) What is the marginal probability of anyone being unemployed?
(c) If you observe that someone is employed then what is the probability he or she
graduated from university?
3. Suppose that competitive cyclists are each tested for banned drugs in 5 independent
tests each year. Suppose that the probability of a cyclist taking banned drugs is
P=0.20.
(a) What is the probability of no positive tests?
(b) What is the probability of at least two positive tests?
4. Suppose that the exchange rate between the Canadian and US dollars is continu-
ously and uniformly distributed this month with a minimum value of 0.97 US dollars
and a maximum value of 1.01 US dollars.
(a) What is the mean value of the exchange rate?
(b) What is the variance of the exchange rate?
(c) What is the probability of an exchange rate greater than 1.00 US dollars?
5. Suppose that the heights of humans in the world are normally distributed with mean
1.5 metres and standard deviation 0.3 metres. Imagine taking repeated samples of 10
people and calculating the mean height Xin each sample.
(a) What is the distribution of X?
(b) In a specific sample what is the probability of finding a mean height above 1.6
metres?
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ECON 250 Full Course Notes
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