Use for statements to find the values of x(t) = 3 cos (2?ft + 0.1) for t = 0,

01, 0.2, 0.3, 0.4 s when f =10, 15, and 20 Hz. Use one set ofstatements to compute the values for all three frequencies and store the results in a two-dimensional array. Use two nested for loops and double indexing.

Suppose X, Y, and Z are independent Gaussian random variables with σx = 0.2, σy = 0.3, σz = 1, μx=3.0, μy=7.7, and μz = 0 Determine the following:

(a) The joint PDF of X, Y, and Z

(b) Pr( (7.6<Y<7.8) | (X<3, Z<0)

c) The Correlation matrix and covariance matrix of X, Y, and Z

The single-index model for stock i is Ri = 0.01+1.5RM + ei. The single-index model for stock j is Rj = 0.02+0.8RM + ej. The standard deviation of the market return is σM=0.2, the standard deviation of ei is σei=0.3 and the standard deviation of ej is σej=0.4. 1. Calculate the systematic risk, firm-specific risk, and total risk of stock i.  

Given the information in the following table, calculate the weight of the active portfolio (w*) if you are trying to create an optimal portolio using the index model.

The following equation represents the weekly demand that a local theater faces.

Qd = 2000 - 25 P + 2 A,

where P represents price and A is the number of weekly advertisements.

Presently the theater advertises 125 times per week. Assuming this is the only theater in town, and its marginal cost, MC, is equal to zero,

a. Determine the profit-maximizing ticket price for the theater.

b. What is the price elasticity of its demand at this price?

c. What is the elasticity of its demand with respect to advertising?

d. Now suppose the theater increases the number of its ads to 250. Should the theater increase its price following this ad campaign? Explain.

Stocks A and B have the following probability distributions of expected future returns:

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 14.00%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 22.91%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.
   

The following are quality control data for a manufacturing process at Kensport Chemical Company. The data show the temperature in degrees centigrade at five points in time during a manufacturing cycle.

The company is interested in using control charts to monitor the temperature of its manufacturing process. Compute the upper and lower control limits for the R chart. (Round your answers to three decimal places.)

UCL=___

LCL=___

Construct the R chart.

12

3 4

Compute the upper and lower control limits for the x chart. (Round your answers to three decimal places.)

UCL=___

LCL=___

Construct the x chart.

12

3 4

What conclusions can be made about the quality of the process?

The R chart indicates that the process variability is  in control/out of control .  - No samples fall/One sample falls/Two samples fall/More than two samples fall...outside the R chart control limits. The x chart indicates that the process mean is  in control/out of control .  No samples fall/One sample falls/Two samples fall/More than two samples fall....outside the x chart control limits.

Dollars and Cents versus a Sense of Ethics   

Grizzly Community Hospital in central Wyoming provides health care services to families living within a 200-mile radius. The hospital is extremely well equipped for a relatively small, community facility. However, it does not have renal dialysis equipment for kidney patients. Those patients requiring dialysis must travel as far as 300 miles to receive care.

Several of the staff physicians have proposed that the hospital invest in a renal dialysis center. The minimum cost required for this expansion is $4.5 million. The physicians estimate that the center will generate revenue of $1.15 million per year for approximately 20 years. Incremental costs, including the salaries of professional staff and depreciation, will average $850,000 annually. Grizzly is exempt from paying any income taxes. The only difference between annual net income and net cash flows is caused by depreciation expense. The center is not expected to have any salvage value at the end of 20 years.

The administrators of the hospital strongly oppose the proposal for several reasons: (1) They do not believe that it would generate the hospital’s minimum required return of 12 percent on capital investments; (2) they do not believe that kidney patients would use the facility even if they could avoid traveling several hundred miles to receive treatment elsewhere; (3) they do not feel that the hospital has enough depth in its professional staff to operate a dialysis center; and (4) they are certain that $4.5 million could be put to better use, such as expanding the hospital’s emergency services to include air transport by helicopter.

The issue has resulted in several heated debates between the physicians and the hospital administrators. One physician has even threatened to move out of the area if the dialysis center is not built. Another physician was quoted as saying, “All the administrators are concerned about is the almighty dollar. We are a hospital, not a profit-hungry corporation. It is our ethical responsibility to serve the healthcare needs of central Wyoming’s citizens.”

Instructions

a. Financial factors and measures. (Compute Payback Period, ROI and NPV - Show all calculations for the supporting calculations. ​)

A shopping center project is proposed to the city council. It cannot be built unless a zoning change is approved by the council. The planning board must first make a recommendation, for or against the zoning change, to the council.
Let A1 = city council approves the zoning change A2 = city council disapproves the change

The prior is: Pr(A1) = .7,   Pr(A2) = .3

Let B denote the event of a negative recommendation by the planning board.

Past history with the planning board and the city council indicates the following

Pr(B|A1) = .2, Pr(B|A2) = .9

3. ____ The planning board has recommended against the zoning change. What is the posterior probability that the city council will approve the zoning change? a) 0.2 b) 0.22 c) 0.3 d) 0.34 e) 0.43


4. ____ You own a local store in the downtown of the city. If the shopping center project is not allowed, your revenue will be $3,000. If allowed, your revenue will be $1,000. The cost of operation is $2,000. Then, you will choose to ______ because your expected profit (or loss if you choose to exit) is ____.

a) Stay, $140 b) Stay, $320 c) Stay, $400 d) Exit, $140 e) Exit, $320