2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given in Table 1.

a) What is the correlation coefficient between the returns on stock A and stock B?

b) What is the expected return and standard deviation of portfolio S which is invested 80% in stock A and 20% in stock B?

c) If you combine portfolio S with a risk free asset paying a return of 4%, what would be the expected return on a new portfolio V if you desire a standard deviation of 27.9%?

d) Plot in mean-standard deviation space the efficiency frontier between Stock A and Stock B, and identify portfolios S and V.

A particular single-machine workstation has a capacity of 1,000 units per day and variability is moderate, such that V = (SCV of arrivals + SCV of effective process time)/2 = 1. Demand is currently 900 units per day. Suppose management has decided that cycle times should be no longer than 1.5 times the average process time.

A) What is the current cycle time in multiples of the process time? (i.e. if the current cycle time was 2 times longer than the process time, put 2 in the answer box)

B) If variability is not changed, what would the daily capacity have to be in order to meet the requirement that average cycle time be no longer than 1.5 times process time?

C) If capacity is not changed, what value would be needed for V in order to meet the requirement that average cycle time be no longer than 1.5 times process time?

THERMODYNAMIC

The specifications of a typical reciprocating internal combustion engine coupled with a
generator are given in Table Q2. With the aid of a P-v diagram, determine the following
engine performance characteristics by using constant specific heat at room temperature:
i) the total mass contained in the cylinder per cycle,
ii) the mass of fuel burned per cycle,
iii) the mean effective pressure,
iv) the engine power in kW, and
v) the specific fuel consumption in g/kWh .

Table Q2
Item Specification
Cycle 4-stroke
Fuel Type Diesel
Fuel Calorific Value 43 MJ/kg
Combustion Efficiency(%) 95
Compression Ratio 19
No. of Cylinder 4
Engine Capacity (cc) 2000
Intake Pressure (kPa) 95 kPa
Intake Temperature (°C) 30
AFR 28:1
Engine Speed (rpm) 1800

Both a call and a put currently are traded on stock XYZ; both have strike prices of $50 and expirations of 6 months.

a. What will be the profit to an investor who buys the call for $4.8 in the following scenarios for stock prices in 6 months? (i) $40; (ii) $45; (iii) $50; (iv) $55; (v) $60. (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign. Round your answers to 1 decimal place.)

b. What will be the profit to an investor who buys the put for $7.5 in the following scenarios for stock prices in 6 months? (i) $40; (ii) $45; (iii) $50; (iv) $55; (v) $60. (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign. Round your ans

. Let xj , j = 1, . . . n be n distinct values. Let yj be any n values. Let p(x) = c1 + c2x + c3x 2 + · · · + cn x ^n−1 be the unique polynomial that interpolates the data (xj , yj ), j = 1, . . . , n (Vandermonde approach).

(a) Remember that (xj , yj ), j = 1, . . . , n are given. Derive the n × n system Ac = b that determines the coefficients ck (as we did in class for n = 4).

(b) Write a MATLAB script that sets up the Vandermonde matrix V for any given vector x.

(c) Find the condition number (infinity norm) of the matrix V where x consists of n = 10, 20, 30, 40 equally spaced points spanning the interval [0, 1]. Report your results in a table of each n

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)

I POST IT TWICE, DONT ANSWER TO BOTH POST. DO NOT COPY YOUR ANSWER TO BOTH POSTS. I NEED TWO DIFFERENT VIEW. Thanks

**DO NOT UPLOAD PHOTOS TO ANSWER MY QUESTION​

*****DO NOT COPY FROM ANY WEBSITE. USE YOUR OWN WORD. DO NOT ANSWER IF YOU ARE NOT COMFORTABLE FOR ANY RESON.

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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?

Data Structures Homework – Singly Linked Lists

Create a singly linked that represents a school. The school has multiple classes. Each class has a different number of students.

class student

{

Long ID;

string Name;

string Address;

float grades[3];

student *below;

};

class Node // the node represents a class in school

{

int ID;

int NoOfStudents;

int NoOfQuizes;

student *t;// a linked list of students is allocated dynamically

Node *Next;

};

class school {

string Name;

Node *Head;

int n;//number of classes in school

};

First, you need to implement the following constructors and destructors:

1- School constructor: Creates an empty school. It takes the school name as a parameter and sets the number of classes to zero.

2- Class (Node) constructor: Sets the class ID, sets the number of students to zero, the NoOfQuizes to zero and the pointers to NULL.

3- Student constructor: Sets the student’s ID, Name and address which are passed as parameters once a student is created.

4- Student destructor: contains the cout statement: ”student destructor is called”

5- Class (Node) destructor: deletes all students in class.

6- School destructor: deletes all the classes in the school.

In your main function create an empty school by entering the name of the school from keyboard (this calls the school constructor), then display the following menu to the user and perform tasks accordingly.

In addition to constructors and destructors, you need to define a function to perform each of the following tasks.

Your program must keep on displaying this list until the user chooses Exit (12).

1. Create a class: This function creates a new class in the school by reading the class information from a text file that has the following format. The class is added to the end of the school linked list. Note that this will call the Node constructor (once)+ the student constructor (multiple times).

Class ID

NoOfStudents

Student ID Student Name Student Address

Student ID Student Name Student Address

Student ID Student Name Student Address

……..

2. Read quiz grades: This function takes the class ID and the number of the quiz (first:0, second:1, Final:2) from keyboard and reads the grades for all students in the class in a certain quiz. Sort the students alphabetically then read their grades (this calls the function sort students (8)).

3. Compute student’s average: Take a student’s ID and return his average

4. Add student: Enter class ID, read a student’s information (ID & name & address from keyboard), add a student to the beginning of the class list. Note that this calls the student’s constructor. Also, read (NoOfQuizes) grades for this student.

5. Delete student: Enter student’s ID, search for the student in the school and delete the student from his class (if found).

6. Delete class: Enter class ID, find the class, delete the list of students in the class (this uses class destructor) then delete the class node from the list (the rest of the school list should remain intact).

7. Sort students: Enter class ID and sort the students of that class based on their names in alphabetical order.

8. Find the student with maximum average in a certain class: Enter class ID, find student with maximum average, then display the student (name + ID).

9. Display student given his name: enter student’s name, find the student and display his ID, grades and average.

10. Display a class given its ID: enter a class ID, find the class and neatly display the information of all the students in that class.

11. Display school: Display all classes in a school. Display each class ID together with its students (ID, name and address of each student).

12. Exit .

In your main function, create a school and test all your work above.

make it clearly thanks..!!