Assignment Three ECON 2040

QUESTION

Assignment Three
ECON 2040
Due Date: A01/A02
23/11/2015, Monday
A03, 24/11/2015, Tuesday

(1) This assignment is to be completed
individually. Students are allowed to
discuss or share ideas with your fellow student however your answer should be
unique and cannot copy others’ work as mentioned in our course outline. Please start working on the assignment right
now, drop by at my office if you have any questions. Otherwise you will not
have enough time to finish the assignment before due date.
(2) Be sure to create a
title page for your assignment, including your name, student number, session number.

(3) Please type the
assignment. Please make effort to present your work professionally.

(4) Questions will be
chosen from the assignment to mark for your final grade. If you do not do
questions that are not chosen to be marked, your marks will be deducted for
number of questions that you did not do.

(5) Please hand in the
printed out assignment before class. No late assignment will be accepted.

Note: the withdraw
deadline without academic penalty
is Nov. 18,2015

1. Redo your midterm if you did any question
wrong. You do not need to hand in your work for this part. Please verify your
answer with the midterm answer key.
2. The following table shows that the economy
next year has three possible states: Good , Average and Poor. It also shows the correponding probability of
each states. The column of stock A shows the investment rate of return (%) for
stock A; and the column of Stock B shows the invesment rate of return for stock
B.

Return (%)

State

Probability

Stock
A

Stock
B

Good

0.4

15

8

Average

0.5

9

10

Poor

0.1

6

12

a)
Calculate the expected value of stock A and B’s return (1 mark)
b)
Calculate the variance of the return of Stock A and Stock B (1 marks)
c)
Calculate the covariance and correlation of Stock A and Stock B’s return ( 2
marks)
d)
An investor invests in 40% of his money in stock A and 60% of his money in
stock B, what is his portfolio’s expected return? What is his portfolio’s
variance and standard deviation? (4
marks)
3.1 Evaluate the following statement. To answer
this question please state the Central Limit Theorem and explain why central
limit theorem is so important. (10 marks)
The
samples mean of a random sample of n observations from a normal population with
mean µ and variance ?2 is a sampling statistics. The sample mean is normally distributed with
mean µ and variance ?2/n due to central limit theorem.
3.2. Find the
sampling distribution of sample means if all possible samples of size 2 are
drawn with replacement from the following population, please calculate the mean
and variance of the sample means.

X

-2

0

2

p(x)

0.2

0.6

0.2

3.3 Let the random
variable X follow a normal distribution with a mean of ? and a standard
deviation of ?. Let1be the mean of a sample of 16 observations
randomly chosen from this population, and2be the mean of a sample of 25 observations
randomly chosen from the same population.

Evaluate
the statement P(? – 0.2? <1< ? + 0.2?) < P(? - 0.2? <2< ? + 0.2?) as to whether it is true or false. ( 5 marks) 4.1. Suppose that the amount of time teenagers spend on the internet is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Construct the 95% confidence interval of the population mean andinterpret what the 95% confidence interval estimate of the population mean tells you. 4.2. A furniture mover calculates the actual weight as a proportion of estimated weight for a sample of 31 recent jobs. The sample mean is 1.13 and the sample standard deviation is 0.16. Calculate a 90% confidence interval for the population mean. 4.3. Suppose that x1and x2are random samples of observations from a population with mean ? and variance ?2. Consider the following three point estimators, X, Y, and Z, of ?: X = (x1+ x2)/2, Y = (x1+ 3x2)/4, and Z = (x1+ 2x2)/3. 1) Show that all three estimators X, Y, and Z are unbiased. ( 2 marks) 2) Which of the estimators X, Y, and Z is the most efficient?( 3 marks) 5. Redo the assignment two computer exercises. Generate 1000 series of data for Bernoulli distribution, Binomial Distribution, Uniform distribution and Normal distribution with the Random Number Generator from Excel as shown in Class. The number of data points for each series can be increased to 200. Then draw the histogram for the sampling mean and see whether this will assemble normal distribution better than the time you did last time, discuss the sampling distribution in terms of mean and variance. After you learn central limit theorem and law of large numbers, how these practices help you to understand these theorems?   ANSWER: REQUEST HELP FROM A TUTOR