(Note: This problem set is for extra practice. It is not for credit, and not to be handed in) Question 1: Suppose that in a study, several measurements were made to determine a particular quantity for different values of . The collected data are summarized in the following table: 1.0000 5.8823 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000 6.0000 8.8823 17.8821 11.8822 14.8826 26.8825 24.8822 28.8822 45.8826 50.8821 59.8829

a) For the

values, determine the measures of central tendency: (a)- Arithmetic mean, (b)- Median, (c)- Mode and the measures of spread: (d)- Range, (e)- Standard deviation, (f)-Variance (g)- Coefficient of variation. Answer: (a)- 26.9733, (b)- 24.8822, (c)- No Mode (d)- 54.0006, (e)- 18.0248, (f)- 324.8950, (g)- 66.8248

b) Apply the least-square regression and fit a first-order line to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy of this linear model with the model in part (a) that only uses the arithmetic mean of the variable . Answer: < 0.8964 , c) Apply the least-square regression and fit a second-order curve to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the accuracy of this polynomial fit with the linear model in part (b). Answer: < 0.9567, > 324.8950

d) Apply the general linear least-square to fit the model , where , and are three basis functions as follow: , , Compute the corresponding matrix system by employing the method of normal equation. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy with part (c). Answer: < 0.9998, >

ECSE 443- introduction to Numerical Methods in EE

Practice Problem Set – Chapter 4

Question 2: The goal of a two dimensional quadratic regression is to find the best values for the coefficients...

...Me1
ProblemSet #2
The US College Enrollment and the “Third Law of Demand”
A theorem proposed by Professors Alchian and Allen in their text, University Economics (1964) has had several rebirths of interest in the literature. The so-called “third law of demand,” or “relative price theorem,” holds that a fixed cost added to a good of varying quality causes the consumer to prefer the category considered of higher quality to the lower.
Recently a number of studies, keeping this theorem in mind have looked into a relationship between the ratio of public to private enrollment and unemployment in cross-sectional as well as in time series data. Part of the full cost of participating in higher education is foregone employment income. In their regression model, these studies have regressed the public/private ENROLLMENT RATIO (as an indicator of relevant demand) against UNEMPLOYMENT RATES (as an indicator of cost) as well as a number of variables designed to account for “other things” which tend to vary at the same time, such as income, financial aid and tuition ratios. Tuition ratio is typically specified as the ratio of the full cost (including forgone employment income) of public higher education (Pa) to private higher education (Pb), where Pa is less than Pb.
In Table 1, below, a cross-sectional model reveals the relationships between relative education demands by public and private university students (as measured by state level ENROLLMENT...

...Yue
Office: KRAN B024A
Office Hours: Monday 12 noon-1 pm &Tuesday 9-10 am.
Phone: 496-1458 email: kyue@purdue.edu
Course goal: We provide a broad overview of the microeconomic aspects of the international economy. We emphasize the development of analytical tools. We also show how we can apply these tools to questions with real-world relevance.
Prerequisites:
Econ 251, Econ 252 (Principles of Microeconomics, Principles of Macroeconomics)
Textbook:
1. Feenstra and Taylor, “International Trade”, 2nd Edition. We follow the textbook very closely in class and cover about 70% of its contents.
2. Yeaple, Study Guide for Feenstra and Taylor’s International Trade, 2nd Edition. We take many practice problems from the Study Guide.
5 copies of the textbook (2nd edition) and 5 copies of the Study Guide (2nd edition) are on reserve at Parrish (the management-and-econ library).
Distribution of homework and other materials:
Katalyst - https://webapps.krannert.purdue.edu/kap/
Course Grades:
Quizzes (best 5 out of 6) 30%
Homework Assignments (best 3 of 4) 25%
Extra Credit Questions 10%
Midterm (in class) 20%
Final Exam 25%
Dates for Quizzes, Homework Assignments, Review Sessions and Exams:
These dates are fixed and will not change. See the class calendar.
Course Materials:
This should be regarded as a likely (but not 100%-certain) schedule as some topics may run shorter or longer than...

...EC 109
Autumn 2011
Dr. Mani
ProblemSet 2
Due Date: Oct31, Monday – between 9 & 11 AM in room S 2.132
Please keep a copy of your assignment and show all your work clearly.
(1) Mr. J. Bond, a retired movie actor, consumes only grapes and the composite good Y (i.e. price of Y is £1). His income consists of £10000 a year from his investment fund plus the proceeds of whatever he sells of the 2000 bushels of grapes he harvests annually from his vineyard in Tuscany. Last year, grapes sold at £2 per bushel and Bond consumed all 2000 bushels of his grapes, in addition to 10,000 units of Y. This year, the price of grapes is £3 per bushel (and the price of the composite good Y is the same as before). If Bond has well-behaved preferences, will his consumption of grapes this year be greater than, less than or the same as last year’s? How about his consumption of the composite good? (Hint: Graph both years’ budget constraints and think about whether last year’s bundle is affordable to Mr. R).
(2) Suppose Carmela’s income is £100 per week, which she allocates between sandwiches and books. Sandwiches cost £2 each. Books cost £10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to £5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than...

...Energy
1. A man climbs on to a wall that is 5 m high and gains 2200 J of potential energy. What is the mass of the man?
Given: Formula:
h = 5 m m = PE/gh
PE = 2200 J
Solution:
m = 2200 J / (9.8 m/s2 x 5 m)
m = 49 kg
2. Calculate the kinetic energy of a 500 kg car travelling at 50 m/s.
Given: Formula:
m = 500 kg KE = mv2/2
v = 50 m/s
Solution:
KE = 500 kg x (50 m/s)2 / 2
KE = 625 000 J
Power
3. Riley climbs a flight of stairs in 3 minutes. If he weighs 700 N and the stairs is 20 m from the ground, how much power will she develop?
Given: Formula:
t = 3 mins = 180 s P = Wd/t
W = 700 N
d = 20 m
Solution:
P = 700 N x 20 m / 180 s
P = 77.8 J/s
4. How much power is developed by a car that runs 80 m/s when the force is equal to 50 000 N.
Given: Formula:
V = 80 m/s W = Fv
F = 50 000 N
Solution:
W = 50 000 N x 80 m/s
W = 4 000 000 J/s
Electricity
5. Charges of 6 and + 4 nC are 3 m apart. Determine the force they exert on each other, and the electric field at a point midway between them.
Given: Formula:
k = 9 x 109 Felec = k q1 q2 /r2
q1 = 6 x 109 C
q2 = 4 x 109 C
r = 3 m
Felec = (9 x 109)(6 x 109)(4 x 109)/32
Felec = 24 x 109 N
6. A 50 cm piece of nichrome wire is used in a home heating element. The cross sectional area of the wire is 0.05 mm2. What is the resistance of the heating element? If it is operated on household current (110 V),...

...GENERAL BIOCHEMISTRY
ProblemSet No. 1
Answered by: Andrea Rose A. Fajardo of BSFT 2-1N
1. Calculate the pH of a dilute solution that contains a molar ratio of potassium acetate to acetic acid (pKa=4.76) of:
a. 2:1
pH = 4.76 + log[2]/[1]
= 4.76 + 0.3010
= 5.06
b. 1:4
pH = 4.76 + log[1]/[4]
= 4.76 + (-0.6021)
= 4.16
c. 6:5
pH = 4.76 + log[6]/[5]
= 4.76 + 0.0792
= 4.81
d. 2:3
pH = 4.76 + log[2]/[3]
= 4.76 + (-0.1761)
= 4.58
e. 9:1
pH = 4.76 + log[9]/[1]
= 4.76 + 0.9542
= 5.71
2. A buffer contains 0.01mol of lactic acid (pKa=3.86) and 0.05mol of sodium lactate per liter.
a. What is the resulting pH of the buffer?
pH = 3.86 + log[0.05]/[0.01]
= 3.86 + 0.6990
= 4.56
b. Calculate the change in pH when 5mL of 0.5M HCl is added to 1L of buffer.
5mL of 0.5 mol/L
5mL * 1L/1000mL = 0.005L
0.005L * 0.5 mol/L = 0.0025mol
NaC3H5O3 = 0.05mol - 0.0025mol = 0.0475
C3H5O3 = 0.01mol - 0.0025mol =0.0075
pH = 3.86 + log[0.0475]/[0.0075]
= 3.86 + 0.8016
= 4.66
• 4.55-4.66 = 0.11 is the change in pH
c. What pH change would you expect if you added the same quantity of HCl to 1L of pure...

...BE 13.8
Vertical analysis (common-size) percentages for Vallejo Company’s sales, cost of goods sold, and expenses are listed below:
VERTICAL ANALYSIS 2012 2011 2010
Sales 100.0% 100.0% 100.0%
Cost of goods sold 60.5 62.9 64.8
Expenses 26.0 26.6 27.5
Net Income 13.5 10.5 7.7
Did Vallejo’s net income as a percent of sales increase, decrease, or remain unchanged over the 3 year period. Provide numerical support for your answer.
Sales – Cost of Goods Sold – Expenses = Net Income
100 – 64.8 – 27.5 = 7.7 for 2010
100 – 62.9 – 26.6 = 10.5 for 2011
100 – 60.5 – 26.0 = 13.5 for 2012
During the 3 year period of 2010-2012, the net income increased as a percent of sales for the Vallejo Company due to the decrease as a percent of sales in both the cost of goods sold and expenses every year.
BE 13.9
Horizontal analysis (trend-analysis) percentages for Spartan Company’s sales, cost of goods sold, and expenses are listed below:
VERTICAL ANALYSIS 2012 2011 2010
Sales 96.2% 104.8% 100.0%
Cost of goods sold 101.0 98.0 100
Expenses 105.6 95.4 100
Net Income (110.4) (88.6) 0
Explain whether Spartan’s net income as a percent of sales increase, decrease, or remain unchanged over the 3 year period.
Sales – Cost of Goods Sold – Expenses = Net Income
100 – 100 – 100 = 0.0 for 2010
104.8 – 98.0– 95.4 = -88.6 for 2011
96.2 – 101.0 – 105.6 = -110.4 for 2012
In 2010, the net income for the Spartan Company is 0. In 2011, the company’s net income decreased as a percent of...

...ProblemSet 1
1. (Star Wars) Real GDP = 461.0(214.5/60.6) = 1,631.76
(E.T.) Real GDP = 399.9(214.5/96.5) = 888.90
(Titanic) Real GDP = 600.8(214.5/160.5) = 802.94
(Shrek 2) Real GDP = 437.2(214.5/188.9) = 496.45
(Avatar) Real GDP = 760.5(214.5/214.5) = 760.5
Real GDP in Order of Largest to Smallest
Movies
Nominal
Box Office Receipts (millions)
CPI in Year Released
Real Box Office Receipts (millions)
Star Wars (1977)
461.0
60.6
1,631.76
E.T. The Extra-Terrestrial (1982)
399.9
96.5
888.90
Titanic (1997)
600.8
160.5
802.94
Avatar (2009)
760.5
214.5
760.50
Shrek 2 (2004)
437.2
188.9
496.45
2. Classify each of the following as employed, unemployed, or not in the labor force.
a. Juanita has two part-time jobs but hopes to get one full-time job instead.
EMPLOYED
b. Bob teaches 1 class at the University at night and volunteers 20 hours a week at the hospital.
EMPLOYED
c. Jaime babysits her younger sister while her mother works.
NOT IN THE LABOR FORCE
d. Emma is retired. She volunteers at the library 10 hours each week.
NOT IN THE LABOR FORCE
e. Alex is 15 years old and hopes to find a part-time job soon but has not applied anywhere.
NOT IN THE LABOR FORCE
f. Rolando is not working but he has submitted an application to work at the local grocery store and is available to start work immediately.
UNEMPLOYED
3. Use the following data to calculate (a) the labor force participation rate, (b) the unemployment rate, and (c) the employment/population...

...ProblemSet 1
Problem 1
Which project should the firm select? Why?
Project B: Managers should try to maximize their stock’s intrinsic value while also bringing in revenue. The P/E ratio shows the dollar amount investors will pay for $1 of current earnings.
Problem 2
If most investors expect the same cash flows from Companies A and B but are more confident that A’s cash flows will be closer to their expected value, which company should have the higher stock price? Explain.
The primary goal of a corporation should be to maximize its owner’s value. If a manager is to maximize shareholder wealth, he/she must know how that wealth is determined. Fundamentally, shareholder wealth is the number of shares outstanding at times the market price per share. A stock’s price at any given time depends on the cash flows a “marginal” investor expects to receive after buying the stock. With that being said, Company A’s cash flow would increase the stock price and the risk would be minimal. Management’s goal should be to make decisions designed to maximize the stock’s price.
Problem 3
The president of Southern Semiconductor Corporation (SSC) made this statement in the company’s annual report: “SSC’s primary goal is to increase the value of our common stock holders’ equity.” Later in the report, the following announcements were made:
a. The company contributed $1.5 million to the symphony orchestra in...

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