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Sat 20 Apr, 2013 07:08 am
I am new to such amazing branch of knowledge of statistics, I have been given first session and I studied but when I try to solve I don't know where to start from in solving for the following questions:
1. The average prices of stock x and stock y for five months are given below:
Stock x: 6 4 1 4 2 Stock y: 3 7 9 4 5
a. Find the correlation coefficient between x and y.
b. Suppose x and y are related to each other by a linear relationship:
y = α0 + α1x
Find estimates of α0 and α1. Now, suppose that x is a function of y (x = β0 + β1y). Find estimates of β0 and β1.
c. Suppose that x and y are returns on investments on stock X and Y with the following means and standard deviations:
STOCK X: Mean return = 3% Standard Deviation = 1%
STOCK Y: Mean return = 3% Standard Deviation = 0.5%
If somebody wants to invest in stock X, what is the probability that he or she will never lose money? Calculate the same probability if he or she wants to invest in stock Y. What conclusion do you get when you compare your results on stock X with your results on stock Y?
d. What is the probability that return on investing in stock X will be greater than 2% and less than 5%?
2. Suppose there are 100 banks in the Middle East, of which 10 are Islamic. Three banks are selected at random (with replacement).
a. Draw a probability tree and insert the probabilities for each branch.
b. What is the probability of the following events?
i. All three banks are conventional.
ii. One is Islamic and the other two conventional.
iii. At least one bank is Islamic.
3. Z has a standard normal distribution. Using distribution table of Z, find the following:
a. P (0 < Z < 1.96) b. P (-1.9 < Z < 0.5) c. Z0.10 d. Z0.25