Find the value of K that minimizes the risk in part (c).

1.  Refer to Example 2.54.

a.  Find Cov(X,Y).

b.  Find ρX,Y .

 

 

2.    Refer to Exercise 18.

a.  Find Cov(X, Y).

b.   Find ρX,Y .

c.    Find the conditional probability density function fY|X (y | 0.5).

d.  Find the conditional expectation E(Y | X = 0.5).

 

3.   An investor has $100 to invest, and two investments between which to divide it. If she invests the entire amount in the first investment, her return will be X, while if she invests the entire amount in the second investment, her return will be Y. Both X and Y have mean $6 and standard deviation (risk) $3. The correlation between X and Y is 0.3.

 

a.  Express the return in terms of X and Y if she invests $30 in the first investment and $70 in the second.

b.  Find the mean return and the risk if she invests $30 in the first investment and $70 in the second.

c.   Find the mean return and the risk, in terms of K, if she invests $K in the first investment and $(100 − K) in the second.

d.  Find the value of K that minimizes the risk in part (c).

e.  Prove that the value of K that minimizes the risk in part (c) is the same for any correlation ρX,Y with ρX,Y ≠ 1.

find the cost of your paper

Determine the outlet concentration x1 in the water solution and in the trichloroethane solution using an analytical equation.

Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….

Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L0 represents the condition for minimum solvent flow rate.

Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent….

Determine the break-point time, the fraction of total capacity used up to the break point, the length of the unused bed, and the saturation loading capacity of the solid.

Drying of Nitrogen and Scale-Up of a Column. Using molecular sieves, water vapor was removed from nitrogen gas in a packed bed (C1) at 28.3°C. The column height was 0.268….