ECON 250 Midterm: ECON 250 Pastmidterm1 Econ250midterm1W10
Economics 250 Mid-Term Test 1
16 February 2010
Instructions: You may use a hand calculator. Do not hand in the question sheet. Answer
all four questions in the answer booklet provided. Show your work. Formulas and tables
are provided at the end of the question pages.
1. A development economist studies the relationship between life expectancy in years (x)
and income per capita in thousands of dollars (y) for three countries and finds the following
(x, y) pairs: (45,15); (78,40); (60,23).
(a) Find the sample means xand y.
(b) What is the sample correlation coefficient between life expectancy and income?
2. Suppose that we know three facts about unemployed workers. First, 30% do not find
a job within the next few months while the remainder do find a job. Second, 15% receive
training while unemployed. Third, 5% both receive training and find a job.
(a) What is the probability of finding a job given that one receives training?
(b) Suppose you observe a worker who has just found a job and exited unemployment.
What is the probability that she or he received training while unemployed?
3. Suppose that a bond can pay an amount $100 with probability 0.75 and a lesser amount
$40 with probability 0.25.
(a) What is the expected value of the amount paid?
(b) An investor is offered a 50% share in this bond for a price of $40, so the profit is
0.5x−40 where xis the payoff described above, that can take on two values. What is the
expected value of the profit?
(c) Suppose you were not absolutely sure of the two probabilities and so wanted to track
other possible values. You denote the probability of a payment of $100 by λand the
probability of a payment of $40 by 1 −λ. Find a formula that gives the expected profit on
a share in this bond as function of λ.
4. Suppose that the probability that any Toyota has faulty brakes when tested is P=0.10.
(a) If a garage tests n= 4 cars what is the probability they find at least 2 with faulty
brakes?
(b) If a second garage tests n= 10 cars what is the probability they find at least two with
faulty brakes?
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ECON 250 Full Course Notes
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Document Summary
Answer all four questions in the answer booklet provided. First, 30% do not nd a job within the next few months while the remainder do nd a job. Third, 5% both receive training and nd a job. (a) what is the probability of nding a job given that one receives training? (b) suppose you observe a worker who has just found a job and exited unemployment. What is the probability that she or he received training while unemployed: suppose that a bond can pay an amount with probability 0. 75 and a lesser amount. with probability 0. 25. (a) what is the expected value of the amount paid? (b) an investor is o ered a 50% share in this bond for a price of , so the pro t is. 0. 5x 40 where x is the payo described above, that can take on two values.
