Calculating Expected Return and Standard Deviation of Combined Investment

[needhelp83]

Let X and Y be the per dollar return of 2 stocks. Suppose that both have an expected return of 0.05, both have a variance of 0.0009 and covariance(X,Y)= -0.001. Suppose that you invest $50 in the stock with return X and $100 in the stock having return Y

1) Calculate the expected return of your combined investment. Calculate the standard deviation

2) Provide the smallest centered at your expected return that will contain your future return with probability 8/9. (HINT: Since you many not assume that the return distribution is normal, you must use Chebychev's theorem)


For number 1) is this simply adding up 0.05 *2??

 

[needhelp83]

1)E[Return] = E[50X] + E[100Y] = (50*.05)+(100*.05)=7.5

The standard deviation is:
Var(Return) = Var(50X+100Y)= 50²Var(X) + 100²Var(Y)+ 2*(50)*(100)*Cov(X,Y) = 1.25

$$\sqrt{1.25}=1.118$$