b) (10) Find values of Adjusted R 2 for the null and the full models from part (a).
Which model is preferred?
R 2Null = 1
R 2Full = 1
Adjusted R 2Null = 1
(1 0.70 )
Adjusted R 2Full = 1
Pump Flow Rate:
Qp = Q6 = 350.26 m3/h
(1) Flow Rate:
vi y re
Q10 = Q9 + Q7 = 9.65 + 13.85 = 23.5 m3/h
Q10 = Q11 + Q12
(Q10)*(10) = (Q11)*(10
vi y re
ENCI 581 PROJECT
In this project, we will designing different components of a municipal wastewate
b) (8) Find the p-value of the test H 0 : = 0.7 vs. H a : 0.7.
1 1 + 0.88686
1 1+ r
2 1 r
2 1 0.88686
Under H 0 ,
1 + 0.70
Critical Value(s): F 0.10 ( 2, 15 ) = 2.70.
Decision: Reject H 0 at = 0.10.
0.05 < p-value < 0.10
( p-value 0.086 )
b) (4) Use a 90% confidence level and Scheffs multiple
(a) [1 points] Write the log-likelihood l( : D) using this parameterization
(b) [11 points] Prove that the gradient of the log-likelihood function with respect to one
of these parameters is given by:
l( : D)
= M E P [1cfw_C i = cij ] E P [1c
(b) The state table is as follows:
A, B = 00
A, B = 01
A, B = 10
A, B = 11
(c) State table with state assignment is as follows:
Next state (Q0*, Q1*)
A,B = 00
A, B = 01
A, B = 10
ECO 171 Industrial Organization
Section 1 - Final Exam
There are 12 short questions and 4 problems. Short
questions are worth a total of 40 points and the problems a total of 60 points.
Answer in the space provided (no need to
Y and X, and a dataset D = cfw_ x, y , . . . , x[m], y[m] We will estimate the model
parameters = [1 . . . n ] by maximizing the following objective function:
f ( : D) = (1 )
Y |X (
: D) +
( : D)
where X|Y ( : D) means the condit
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11. (3 pts) Which of the following is true?
A conjugate base will always have a pKb > 7.
H2O is the conjugate acid of H3O+.
A Bronstead-Lowry base is a proton acceptor.
A Lewis acid is an electron pair donor.
4. A monopolist is trying to solve its optimal second degree price discrimination (prices and package sizes) and confronts two dierent type of consumers cfw_l, h with demand functions:
= 8 qh
= 4 ql .
There are twice as many consumers of the low typ
11. A merger between two rms selling goods that are substitutes will lead
to lower prices as it allows the rms to coordinate their pricing. True
or False. Explain.
12. Collusion between two rms is possible no matter what their marginal
cost dierence is.
6. In a Cournot model the rms residual demand function is more elastic
than total industry demand. True or False. Explain.
7. Suppose that an industry with 20 rms has a Herndahl index of 500.
What can you conclude about the four-rm concentration ratio?
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Final Exam, Form C
There are 15 pages and 60 questions of equal value in this exam
DO NOT OPEN UNTIL INSTRUCTED.
The exam will end at 8:00 pm.
Mark down your test form (A, B, C or D)
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Part II: Multiple Choice, Short Calculations
Circle the correct answer and circle your response on the cover No partial credit
14. (6 pts) Which of the following represents a saturated solution?
i. [Ca2+] = 1.0 x 10-4 M; [SO32-] =
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Part III: Long Answer
Please show all work Partial credit
23. (20 pts total) Consider the reaction at 25oC:
CaO(s) + CO2(g)
H f (kJmol )
6. Consider the Hotelling model. The beach is 2 miles long and the monopolist has one shop at each extreme (one at the extreme left and the other at
the extreme right). Transportation cost per mile (going back and forth)
is t = 1. Consumers are willing to
4. [21 points] Inference
Consider a chain probabilistic network X1 X2 Xn and a corresponding clique
tree of the form C 1 C n1 where Scope[C i ] = cfw_Xi , Xi+1 . Each variable Xi has
|Val(Xi )| = d possible values. In this question we will c
Yi |Ki , 1 , 2 , . . . , L
multinomial ( Ki )
Dirichlet(1 , . . . , M )
(a) [2 points] Draw the full graph for N = 3 and L = 2.
(b) [5 points] Given the context K = k nd a minimal set D Y i such that the
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19. (6 pts) Consider the following reaction:
CO (g) + 2 H2 (g)
The value of Kc for the reaction is 14.5 at 483 K. At equilibrium, the concentrations
of CO and CH3OH are 1.03 M and 1.56 M, respectively. Calculate the conce