Download AEA41 Examination One

AEA41
Examination One
page 1 of 9
AEA41 Examination One
Indicate the correct answer on the accompanying answer sheet.
There will be no negative grading.
1. The summation expression corresponding to the sum 1 + 2 (the sum of two terms in an
increment of one) is:
1
A:
i
i 1
3
B:
i
i2
2
C:
x
i 1
D:
None of the above.
2. The summation expression corresponding to the sum 1 + 2 + .. + 100 (the sum of 100
terms in increments of one) is:
100
A:
x
i 1
99
B:
i
i 0
100
C:
x
D:
None of the above.
i
i 1
2
3. The summation expression
 x is equivalent to:
i 1
A:
B:
C:
D:
2xi
2xj
2x+2
None of the above.
2
4. The summation expression
 10
2
is equivalent to:
i 1
A:
B:
C:
D:
20
400
(210)2
None of the above.
5. A continuous random variable x is distributed uniformly over the interval x = 100, x =
200. The intersection of the probability density function for x and the (x) axis is:
AEA41
Examination One
page 2 of 9
A:
B:
C:
D:
1/10
100
200
None of the above.
6. A continuous random variable x is distributed uniformly over the interval x = 100, x =
200. The height of the probability density function for x at the point x = 150 is:
A:
B:
C:
D:
100
200
1/10
None of the above.
7. A continuous random variable x is distributed uniformly over the interval x = 100, x =
200. The probability of the outcome x < 100 is equal to:
A:
B:
C:
D:
1.0
0.1
0.01
None of the above.
8. A continuous random variable x is distributed uniformly over the interval x = 100, x =
200. The probability of the outcome x > 100 is equal to:
A:
B:
C:
D:
0.1
0.01
0.001
None of the above.
9. A continuous random variable x is distributed uniformly over the interval x = 100, x =
200. The probability of the outcome x > 120 is equal to:
A.
B.
C.
D.
0.25
0.50
0.75
None of the above.
10. A continuous random variable x has the probability density function (x) = Cx, for 0
< x < 10 and (x) = 0 otherwise, where C is an unspecified constant. The value of C that
ensures that (x) constitutes a true probability density function is:
A.
B.
C.
D.
1
2
10
None of the above.
AEA41
Examination One
page 3 of 9
11. A continuous random variable x has the probability density function (x) = x, for 0 <
x < C and (x) = 0 otherwise, where C is an unspecified constant. The value of C that
ensures that (x) constitutes a true probability density function is:
A.
B.
C.
D.
10
20
100
None of the above.
12. A discrete random variable x has the probability density function (x) = .5 when x =
0 and (x) = .5 when x = 1. The expected value of the random variable E(x)  i xi (xi)
is:
A.
B.
C.
D.
0
1
.75
None of the above.
13. A discrete random variable x has the probability density function (x) = .5 when x =
0 and (x) = .5 when x = 1. The variance of the random variable V(x)  i (xi – E(x))2
(xi) is:
A.
B.
C.
D.
0
1
.75
None of the above.
14. A normally distributed random variable x has expected value  = 10 and variance 2
= 1. If x represents output from a production process that is sold in the market at a perunit price p = 10, then the revenue from the enterprise has, respectively, mean and
variance (mean, variance):
A.
B.
C.
D.
(10, 1)
(10, 10)
(1, 10)
None of the above.
15. A normally distributed random variable x has expected value  = 10 and variance 2
= 1. If x represents output from a production process that is shared equally among three
firms and then sold in the market at a per-unit price p = 1, then the revenue that each firm
receives from the enterprise has, respectively, mean and variance (mean, variance):
A.
B.
C.
D.
(1/3, 1)
(1/3, 3)
(1/3, 1/9)
None of the above.
AEA41
Examination One
page 4 of 9
16. A firm produces product q which it sells in a market. Demand in the market is given
by the linear demand function p = 12 – q. If its objective is to maximize revenue by
selecting the optimal amount of output to produce, then it faces the constraint that the
only price quantity combinations that are relevant are those that lie on the demand
function. The stationary point for the revenue function is q equals
A.
B.
C.
D.
0
12
2
None of the above.
17. Using the Nth-order derivative rule for characterising the stationary point, we find
that the first non-zero derivative at the stationary point is
A.
B.
C.
D.
The first derivative.
The fourth derivative.
The sixth derivative.
None of the above.
18. At the stationary point where (x) = 0, we find that the first non-zero derivative at
the stationary point is
A.
B.
C.
D.
A minimum.
A maximum.
A point of inflection.
None of the above.
19. A farmer with D = 400 metres of fencing wishes to maximize the total area enclosed
by the fence. If we restrict choices to rectangles with width w and length , then the
equation for the line that locates the stationary point is
A.
B.
C.
D.
(w)  200 – 4w = 0
(w)  200 – 4w2 = 0
(w)  400 – 2w = 0
None of the above.
20. A firm facing demand p(q)  301 – q2 produces with costs C(q)  q. In the range
where quantity is non-negative the firm maximizes profit,   p(q)  q – C(q), by
rationalizing
A. The stationary point is q = 12 where the first non-zero derivative is the second
derivative and is negative. Hence, the best thing to do is to produce at q = 12.
AEA41
Examination One
page 5 of 9
B. Because at the stationary point q = 10 the first non-zero derivative is the third
derivative, the stationary point is a point of inflection and the profit maximum is obtained
at the intersection of the demand function and the q axis (q = 301  17.3494).
C. Because at the stationary point q = 10 the first non-zero derivative is the second
derivative and its value is negative, the best thing to do is to produce at the point q = 10.
D. None of the above.
AEA41
Examination One
page 6 of 9
AEA41
Examination One
page 7 of 9
AEA41
Examination One
page 8 of 9
AEA41
Examination One
page 9 of 9
Name
Answers
1.
D
2.
D
3.
D
4.
D
5.
D
6.
D
7.
D
8.
D
9.
D
10.
D
11.
D
12.
D
13.
D
14.
D
15.
D
16.
D
17.
D
18.
D
19.
D
20.
C