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Econ 299 Winter 2017
L. Priemaza
University of Alberta
Econ 299
Assignment #3
Winter 2017
L. Priemaza
1) Consider a six sided die with “Win” on two sides, “Lose” on 1 side, and
“Tie” on 3 sides for the following questions:
What is the complement event to “Win”?
How are “Lose” and “Tie” related?
From (b), calculate P(Lose or Tie).
Calculate the probability of rolling “Win” twice in a row.
Assume that rolling “Win” wins you $30, rolling “Lose” loses you $30, and
in a tie nothing happens. Calculate the expected value, variance, and
standard deviation of playing this game.
f) Assume instead that rolling “Win” wins you $80, rolling “Lose loses you
$40, and in a tie you lose $20. Calculate expected value, variance, and
standard deviation of playing this game.
g) Analyze and compare the ANSWERS from (e) and (f). Call (e) Game 1
and (f) Game 2.
a)
b)
c)
d)
e)
2) A recent poll of Loricstan asked an entire population what their favorite pet
(P) was - a dog(D) or fish (F) - and questioned them (Q) if they were afraid
of the water (A) or not (N). The joint pdf’s are as follows:
Afraid of Water (A)
Not afraid of water (N)
Dog (D)
0.17
0.43
Fish (F)
0.3
0.1
a)
b)
c)
d)
Calculate all marginal probabilities.
Calculate f(D|Q=A).
Calculate f(A|P).
From c, are P and Q statistically independent? Why or why not?
Don’t forget the lab exam Tuesday April 11th.
Tuesday lab students will write the exam at 4pm, and
Wednesday lab students will write the exam at 2pm. You
will need a non-returnable USB drive for the exam.
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Econ 299 Winter 2017
L. Priemaza
3) Often laptops have an issue with overheating and frying the connections to
various components, especially the wireless modem. Typically faster
laptops without adequate cooling have this issue. Refer to the following
table’s sample data for budget laptops:
Observation
1
2
3
4 Year Modem Failure
11
24
10
rate (F - %)
Laptop speed (S-GHz)
2.4
2.6
1.9
a) Calculate sample mean of F and S.
b) Calculate variance and standard deviation of F and S.
c) Calculate covariance and correlation between F and S. Interpret.
d) Create and interpret a 95% confidence interval for the mean of F.
e) Test the hypothesis that the average failure rate is 10% (α=10%)
f) Use OLS to estimate the following equation, including predicted values
and residuals.
Fi  1   2 Si   i
4) Answer the following:
a) What error term assumptions are essential to use OLS to estimate
relationships between variables?
b) Briefly describe why OLS is BLUE (proofs not needed).
c) Explain when a null hypothesis is accepted.
d) How many chicken wings I eat is normally distributed with a mean of 12
and a standard deviation of 1.5. Calculate the probability that I eat more
than 14 chicken wings.
e) From (d), what is the maximum amount of chicken wings I eat during the
7% lowest wing nights?
f) What is the critical chi-squared value that cuts of 2.5% of the tail with 55
degrees of freedom?
g) What is the critical F value that cuts off 1% of the tail with 7 degrees of
freedom in the numerator and 70 degrees of freedom in the
denominator?
Assignment is due in the Economics Main Office by 3:45pm Wednesday, April 5th, 2017. It is
the student’s responsibility to deposit the assignment in the assignment box. Late assignments
(up to 24 hours) will be penalized 15% and must receive a time stamp.
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