Consider the following regression model: Yi = αXi + Ui , i = 1, .., n (2)

The error terms Ui are independently and identically distributed with E[Ui |X] = 0 and V[Ui |X] = σ^2 .

1. Write down the objective function of the method of least squares.

2. Write down the first order condition and derive the OLS estimator αˆ.

Suppose model (2) is estimated, although the (true) population regression model corresponds to: Yi = β0 + β1Xi + Ui , i = 1, .., n with β0 different to 0.

3. Derive the expectation of αˆ, E[ˆα], as a function of β0, β1 and Xi . Is αˆ an unbiased estimator for β1? [Hint: Derive first E[ˆα|X].]

4. Derive the conditional variance of αˆ, V[ˆα|X], as a function of σ^2 and Xi .

An electric vehicle has the following parameter values:

m_v = 800kg

C_D =0.2

A_f = 2.2 m²

ρ = 1.18 kg/m

f r = 0.008 + 0.6×10^-6×v² (v: vehicle speed in m/s)

The vehicle is on level road. It accelerates from 0 to 100 km/h in 10s such that its velocity profile is given by v (t) =0.29055t² for 0 < t < 10s. (The mass factor is assumed unit)

a. Define the traction force expression F_t

b. Sketch F_t versus time

c. Define the instantaneous traction power expression

d. Calculate the energy consumed during the acceleration (0 < t < 10s)

e. Calculate the energy lost for non-conservative forces (wind and rolling resistance)

f. Find the change in kinetic energy and the change in tractive energy during acceleration.

Partial Differential Equations

(a) Find the general solution to the given partial differential equation and (b) use it to find the solution satisfying the given initial data.

Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u

u(x, x) = e −x 2

Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y

u(0, y) = 1 + y 2

Exercise 3. y ∂u ∂x + x ∂u ∂y = 0

u(x, 0) = x 4

Exercise 4. ∂u ∂x + 2y ∂u ∂y = e −x − u

u(0, y) = arctan y

Exercise 5. ∂u ∂x+v ∂u ∂y = −ru

(here r and v 6= 0 are constants) u(x, 0) = sin x x

POST #2 (ANSWER ONE OF THE QUESTIONS)

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***PLEASE JUST ANSWER THE QUESTION. IT NEED TO BE 150 WORDS.

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Instructions:

Watch the following videos, then answer ONE of the questions below: (150 WORDS)

https://www.youtube.com/watch?time_continue=15&v=9Os7LDOOJao

https://www.youtube.com/watch?time_continue=1&v=BzWWL2LXoNk

Discussion Questions:

How was America affected by the Cold War?

Why did the policy of “containment” develop and what were its goals?

How did the fear of Communism and the “red scare” affect American society during the 1950s?

The United States federal personal income tax is calculated based on filing status and taxable income. There are four filing statuses (in this program we’ll use only three): single filers, married filing jointly, and head of household. The tax rates vary every year. Table 1 shows the rates for 2016. If you are, say, single with a taxable income of $10,000, the first $9,075 is taxed at 10% and the other $925 is taxed at 15%. So, your tax is $1,046.25.

Table 1. 2014 Taxable Income Brackets and Rates

Rate

Single Filers

Married Joint Filers

Head of Household Filers

10%

$0 to $9,075

$0 to $18,150

$0 to $12,950

15%

$9,076 to $36,900

$18,151 to$73,800

$12,951 to $49,400

25%

$36,901 to $89,350

$73,801 to $148,850

$49,401 to $127,550

28%

$89,351 to $186,350

$148,851 to $226,850

$127,551 to $206,600

33%

$186,351 to $405,100

$226,851 to $405,100

$206,601 to $405,100

35%

$405,101 to 406,750

$405,101 to 457,600

$405,101 to $432,200

39.6%

$406,751+

$457,601+

$432,201+

Source: Internal Revenue Service

Part I:

You are to re-write programming assignment 1 to compute personal income tax. Your program should prompt the user to enter the filing status and taxable income and compute the tax. Enter 0 for single filers, 1 for married filing jointly, and 2 for head of household.

Part II:

In this part of the assignment, you will reorganize your code using Methods. Your program must have at least four (4) methods i.e the main method, and the other three (3) for tax brackets that return the tax amount owed. You will organize the income ranges as an Array in each method and select an Array Record to compute specific tax in a tax bracket.

Part III

i) You are required to follow the Software Development Process (Ref: Chapter 2.16).

ii) Must include a Design Diagram [Ref: Fig. 6.11]

iii) Use UML [Ref: Fig 9.4] create class diagrams for your program

NOTE

There will be NO POINTS earned even if your code is working if you

1. don’t use methods

2. don’t use arrays

Hence you will get a 0/50.

Deliverables:

Note:

· Project name: ProgrammingAssignment_2

· Class name: ProgrammingAssignment_2

all persons mentioned below are New Zealand tax residents unless otherwise stated. All taxpayers have a 31 March balance date.

QUESTION 1. Tobby has been buying and selling residential houses since 2010 and is regarded as a land dealer for tax purposes. Tobby also owns 20% and his daughter (who is 22 years old) owns 5% of Tobby Rentals Ltd (the balance of 75% is owned by his close friend Fred), a company that invests in residential rental investment properties. In January 2012, the company bought a rental property. In December 2016, the company decided to sell the rental property for a very good price. You are required to explain whether the income from the sale of the property by Tobby Rentals Ltd is taxable income under sections CB 6, CB 9 and CB 6A.

QUESTION 2. Kim is married to Bruce, a property developer. Kim is settlor and trustee of a trust, which owns all the shares in Kim's family company, Guts Ltd. Guts Ltd recently sold a rental property which was bought nine years ago. Is the income derived by Guts Ltd assessable income under section CB 10?

QUESTION 3. Maryanne entered into a sale and purchase agreement on 15 October 2015 to buy a property in Auckland with the intention of providing a home for herself and her children. When she eventually sells it, she hopes to make a gain and leave her children a legacy. The title of the property was registered in her name on 15 December 2015. However, in April 2017, she got a new job in Wellington and entered into an agreement to sell the property on 1 May 2017 to move closer to her new job. Property prices have risen, so Maryanne is able to sell the house for much more than she paid for it. The title was registered in the buyer’s name on 1 July 2017. You are required to explain whether the income from the sale of the property by Maryanne is assessable income under sections CB 6 and CB 6A (show also which dates are relevant in arriving at your decisions). She is not associated with a land developer/divider or dealer or builder.

Multiple Choice

• -4.42%

• 4.63%

• 4.16%

• 5.55%

• 5.09%