a. Test the hypothesis that the mean return for portfolio A during 2011-2019 is no different from the mean return on government’s T-Bill of 2.6% for the same time period.

b. Test the hypothesis that the mean return for portfolio B during 2011-2019 is no different from the mean return on government’s T-Bill of 2.6% for the same time period.

c. Test the hypothesis that the mean returns of the two portfolios are not statistically different from each other.

d.  Test the hypothesis that the risk of the two portfolios (measured by the variances of the returns) are not statistically different from each other.

e.  A financial analyst claims that portfolio A has higher performance than portfolio B.  Test for the claim of the financial analyst? Do you agree?

3.  Given the distribution of the following variable (X), find the mean, E(X), and the variance V(X) of the variable X.

X: 10,    6,   5, 8,  3, 4, 4.5

Probability: .1, .15,  .3,      .2, .05, .1, .1

a.   E(X) = __________________

What does E(X) represent?  ________________________________________________

b.   V(X) =   ____________________

What does V(X) represent?  ________________________

c. Y is a variable with E(Y) = 5, V(Y) = 82, and E(XY) = 15.2 .

d.  Find E(Z), where Z = 10X + 3Y  ____________________________________

e.  Find V(Z). _______________________________

f.  Find covariance of X and Y. __________________

g.  Find the correlation coefficient between X and Y.

4.  Given that E(X) = 5, E(Y) = 8, E(X²) = 68, E(Y²) = 75 and r_x,y = .35, find the followings.

a.  Find V(X) _________________ b. Find V(Y) _________________

c. Find E(5 + 3X) ____________ d. Find E(2X - 2Y) _____________

e. Find E(5XY) _______________ f. Find E(3X²)__________________

g. Find V(2 + 4Y) ____________ h. Find V(5X - 2Y) _____________

i. Find V(X*Y) _______________ j. Find Cov(X,Y) _________________