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Name: EC
2
303 Foundations for Econometrics
Matriculation #: PS2
Tutorial Section (W#):
Week 4: Problem Set 2
DUE: Monday 9 September,
1
2pm
• Please hand in to the economics office (AS2 – L6)
• Late assignments will not be accepted.
• Show your work to get full credit.
• Carry through fractions or exact decimals when possible. You can
round final answers to two decimal places.
1. (4 pts) X and Y are discrete random variables with the following joint distribution:
Value of Y
14 22 32 40 65
2 0.05 0.02 0.10 0.03 0.01
Value of X 5 0.17 0.15 0.05 0.02 0.01
8 0.02 0.03 0.15 0.10 0.09
That is, P(X = 2, Y = 14) = 0.05, and so forth.
(a) Calculate the probability distribution, expected value, and variance of X.
Calculate the probability distribution, expected value, and variance of Y.
(b) Are X and Y independent? Justify your answer.
For the next two problems, review the last lecture slides from W4 or see Section 4.7
of the textbook
(c) Calculate the probability distribution and mean of Y given X = 8.
(d) Let W denote a random variable such that W = 2X + Y . Compute E(W) and
V ar(W)
1
EC2303 – Foundations for Econometrics Version: September 3, 2013
2. (3 pts) Suppose that all five-card poker hands (C525 ) are equally likely (no jokers). What
is the probability of being dealt the following hands?
(a) A flush (all five cards are the same suit)
(b) 1 pair (a, a, b, c, d – where a, b, c, d are all distinct)
(c) Straight (a, a + 1, a + 2, a + 3, a + 4) – that is, 5 consecutive cards such that not all
cards are the same suit (that would be a straight flush). Note that an ace can count
as the lowest or highest card in a straight – either (ace, two three, four, five) or (ten,
jack, queen, king, ace).
3. (2 pts) Suppose people enter a shopping market at the rate of 1 person every 2 minutes.
(a) What is the probability that no one enters between 10:15am and 10:20?
(b) What is the probability that at least 4 people enter between that same time?
Feel free to use a probability table for both (a) and (b)
4. (1 pt) Suppose you are dealt a hand of 13 playing cards. What is the probability that your
hand is completely missing at least 1 suit?
Note that the answer is not
C41C
39
1
C5213
2
