The rates of return of Stock A and B are distributed as follows:

State Probability Return on A Return on B

1 0.3 15% 5%

2 0.5 9% 7%

3 0.2 -1% 12%

Suppose you have invested $1000 in stock A and $2000 in Stock B. Please, find this portfolio’s expected return and total risk. What is the correlation between the rate of return on Stock A and Stock B?

An elastic (stretchable) balloon made of a material that is permeable to water but not to any solutes is filled with an aqueous solution containing 0.1 M glucose and 0.3 M NaCl. The balloon is then sealed and completely immersed in an second aqueous solution with NaCl as the only solute. The balloon does not expand or contract. What is the concentration of NaCl in the solution that the balloon was immersed in (the second solution)? Assume all salts undergo complete dissociation.

. Air enters the compressor of an ideal gas refrigeration cycle at 7oC and 40 kPa and the turbine at 37oC and 170 kPa. The mass flow rate of air through the cycle is 0.3 kg/sec. Assuming variable specific heats for air, determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Also, draw the T-s diagram of the gas refrigeration cycle.

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset?

Fluids of viscosities μ1=0.15 N‐s/m2 and μ2=0.18 N‐s/m2 are contained between two plates (each plate is 0.85 m2 in area). The thicknesses are h1=0.6 mm and h2=0.3 mm, respectively. Find the force F to make the upper plate move at a speed of 1.5 m/s. What is the fluid velocity at the interface between the two fluids?  

Ebenezer Scrooge has invested 50% of his money in share A and the remainder in share B. He assesses their prospects as follows:

A B

Expected return (%) 18 19

Standard deviation (%) 20 24

Correlation between returns 0.3

a. What are the expected return and standard deviation of returns on his portfolio?

b. How would your answer change if the correlation coefficient were 0 or –0.30?

You’ve identified a comparable firm for a new division you are heading up. The comparable has an equity beta of 1.4 and its debt has a beta of 0.3. The equity of the comparable has a market value of $30B and has $4B in debt outstanding. The market risk premium is 6% and the risk-free rate is 2%. What is the appropriate discount rate to use for your division’s assets/projects?

There are two traffic lights on a commuter's route to and from work. Let X₁ be the number of lights at which the commuter must stop on his way to work, and X₂ be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X₁, X₂ is a random sample of size n = 2).

(a) Determine the pmf of T_o = X₁ + X₂.

(b) Calculate μ_To.
μ_To =  

How does it relate to μ, the population mean?
μ_To =  · μ

(c) Calculate σ_To².

How does it relate to σ², the population variance?
σ_To² =  · σ²

(d) Let X₃ and X₄ be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T_o = the sum of all four X_i's, what now are the values of E(T_o) and V(T_o)?

(e) Referring back to (d), what are the values of

P(T_o = 8) and P(T_o ≥ 7)

[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)

DataSpan, Inc., automated its plant at the start of the current year and installed a flexible manufacturing system. The company is also evaluating its suppliers and moving toward Lean Production. Many adjustment problems have been encountered, including problems relating to performance measurement. After much study, the company has decided to use the performance measures below, and it has gathered data relating to these measures for the first four months of operations.

Management has asked for your help in computing throughput time, delivery cycle time, and MCE. The following average times have been logged over the last four months:

Required:

1-a. Compute the throughput time for each month. (Round your answers to 1 decimal place.)

1-b. Compute the manufacturing cycle efficiency (MCE) for each month. (Round your answers to 1 decimal place.)

1-c. Compute the delivery cycle time for each month. (Round your answers to 1 decimal place.)

3-a. Refer to the move time, process time, and so forth, given for month 4. Assume that in month 5 the move time, process time, and so forth, are the same as in month 4, except that through the use of Lean Production the company is able to completely eliminate the queue time during production. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

3-b. Refer to the move time, process time, and so forth, given for month 4. Assume in month 6 that the move time, process time, and so forth, are again the same as in month 4, except that the company is able to completely eliminate both the queue time during production and the inspection time. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)