econ2040 economic assginment

QUESTION

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 statementP(?
– 0.2? <1< ? + 0.2?) REQUEST HELP FROM A TUTOR