## econ2040 economic assginment

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 Bâs 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 Bâs 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

portfolioâs expected return? What is his portfolioâs 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 Âµ and

variance ?2 is a sampling statistics. The sample mean is normally distributed with

mean Âµ 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?)

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