A current filament carrying 8A in the z a direction lies along the entire z-axis in free space.
A rectangular loop connecting A (0, 0.2, 0) to B (0, 0.2, 0.3) to C (0, 0.7, 0.3) to D (0, 0.7,
0) to A lies in the x = 0 plane. The loop current is 3 mA and it flows in the z a direction in
the AB segment. Find the force on the loop due to the field of the straight filament.

What is the expected output from the following program (3 answers)

______­­ ______namespace std; double insurance(int); void main() { int j; ______ mileage; ______ monthly_rent; for (j=______ j<4; j++) { mileage=1000*j; monthly_rent= 0.3*mileage + insurance(mileage); printf("Monthly rent for %4d.2f is : $ ______ . \n", mileage, monthly_rent); } } double insurance(int miles) { double mileage_charge; if (miles<=1000) { mileage_charge=100.0; }___ if ((miles>1000) && (miles<=2000)) { mileage_charge=150.0; }; ___ (miles>2000) { mileage_charge=200.0; }; return(mileage_charge);

8. For each of the following, identify the distribution based on the MGF. Be sure to specify name of distribution and value(s) of parameter(s).

(a) MX(t) = (0.3 + 0.7 e t ) 9 , t ∈ (−∞,∞).

(b) MX(t) = 0.8 e t + 0.2, t ∈ (−∞,∞).

(c) MX(t) = e 9(e t−1), t ∈ (−∞,∞).

(d) MX(t) = 0.75e t 1−0.25e t , t < − ln 0.25.

(e) MX(t) = 0.4e t 1−0.6e t 20, t < − ln 0.6.

Suppose that an investor has a choice between investing in a bond fund (B) and a stock fund (S).

The bond fund has an expected return of E(rB) = 0.06 while the stock fund has an expected return of E(rS) = 0.10. The standard deviation of the bond fund is ?B= 0.12 and the standard deviation of the stock fund is ?S = 0.25.

(a) Calculate the expected return and standard deviation for each of the following portfolio weights. If you are comfortable using EXCEL you can use the “Portfolio Weight Calculator” (located in Cat Courses) to complete the table. When inputting the values do not use decimals (e.g. The expected return of the bond fund is inputted as 6 not 0.06). You do not have to show your calculations.

(b) Plot the expected return and standard deviation of the various portfolios using EXCEL (draw the investment opportunity set). Identify the minimum variance portfolio (MV Portfolio)

(c) Prove that an investor would never choose a portfolio that has a weight of 10% equity fund and 90% bond fund.

Exercise 10.2.5: Setting the threshold for biometrics.

A biometric authentication system using fingerprints returns a value between 0 and 1 for each attempted match. The system was tested with 1000 genuine fingerprints and 1000 imposter fingerprints. The histogram shows the numbers of genuine and imposter attempts for different ranges.
Ex: 88 of the 1000 genuine fingerprints returned a value of n between 0.5 and 0.4, while only 3 imposter fingerprints returned a value in the same range.

(a)

Determine the threshold value of n such that less than 1% of imposter attempts are accepted. How many false alarms are generated as a result?

(b)

Determine the threshold value of n such that less than 1% of genuine attempts are rejected. How many imposter attempts are accepted as a result?

(c)

Determine the threshold value of n such that no genuine attempts are rejected. How many imposter attempts are accepted as a result?

OfficeComfort manufactures three ergonomic chair: Basic, Deluxe, Contemporary

It has four departments: Assembly, Finishing, QualityControl, Packaging with number of workers (12, 3, 20, and 2 respectively).

• The company works one shift of 8 hours
• Management has set minimum production numbers for each product in order to maintain staff proficiencies. Each product must make up at least 20% of total production.
• Demand exceeds capacity for all products

1. Consider the following production function for bus transportation in a particular city:

Q= a

Where Fuel input in gallons = F

Capital input in number of busses = K

Labor input in worker hours = L

Output in millions of bus miles = Q

We estimate the various parameters as follows using historical data:

                                    α=0.0012, β1=0.45, β2=0.2, β3=0.3

a) Determine output elasticities for Labor.

b) Suppose that labor hours increase by 10%. By what percentage will output increase?

Pioneer Castings, Inc. is realizing it's employee turn-over is rather high. Furthermore, the management is also wondering if the rates are the same between Men and Women. To find out the details, it randomly picked a sample of men and women and recorded the number of years each stayed with the company. Given this dataset, can we conclude that the men and women have the same tenure at the company? Use level of significance = 4% everywhere.                  
                                      
                  
Run the appropriate T-test (using Excel and Explain the steps). Output to Cell D33.                              
Q5   What is the P-value?              
Q6   What is the Level of Significance?              
Q7   If you compare the T-stat with T-critical, you would conclude that               
Q8   If you compare the P-value with Alpha, you would conclude that               

Men       Women
3.2       0.7
15.7   0.9
1.3       0.8
0.7       0.3
8.6       5.8
10.4   2.3
3.2       1.4
1.3       9.3
23.9   5.7
0.2       12.1
0.8       2.8
11.1   0.4
1.5       1.4
3.7       1
14.9   0.8
3       11.9
2.3       4.8
18.2   1.3
12.9   2.6
2.5       1.8
3.8       6.3
3.4       20.7
5.5       1.8
3.8       16.4
17.3   4.1
3.7       2.7
9.7       1.4
10.3   2.9
4.3       4.5
9       4
15.8   0.6
16.8   3
4.1       1.1
5.6       7
1.4       1.4
20.1   2.3
1.2       17
5.1       6
5.8       3.7
6.8       6.8
13.7   6.1
6.1       0.4
6.4       4.9
2.5       3.3
22.2   10.6
4.4       4.9
18.1   0.3
0.4       4.7
2.8       3.7
13.9   1.4
7.9       2.8
5.4       1.3
6.2       1.6
2.5       4
11.3   7.1
10       2.5
2       3.8
1.5       5.8
4.3       8.9
1.3       7.6
5.8       11.2
2.8       3.2
1.5       9.4
0.6       5.6
5.8       8.2
4.8       0.1
2.7       2.5
5.7       11.1
17       2.8
11.3   1.1
9.6       3.5
1.9       2.2
15.8   2.9
2.4       1.6
5.6       6.6
0.9       1.9
20.6   1.3
11.2   1.7
10.6   7.8
1.2       5.3
10.7   3.1
3.1       5.2
0.2       7.6
0.5       0.6
3.7       5.6
7.1       2.2
1.6       10.5
20.1   2.8
3.8       8.5
3.6       6.2
1.8       1.5
1.4       3.4
11.3   8.9
10.2   20.2
11.6   0.6
15.9   2.5
15.3   3
10.1   0.7
3.4       10.7
3.7       0.3
6.4       4.1
14.2   35.9
2.2       7.1
2.6       4.2
18.9   3.2
6.4       1.4
12       2
16.6   2
7.3       20.9
5.3       25.2
10.3   1.4
16.7   5.2
12.6   2.9
1.9       3
7.1       2.5
6.6       6.1
1.6       12.4
3.2       3
1.6       8.4
0.9       0.8
0.5       13
1.5       1.5
1.9       1.1
4.8       5.9
18       8.4
1       10.6
0.8       4.2
16.5   0.6
1.6       17.6
3.1       1.4
0.6       4.7
10.8   15.4
1.2       8.6
3.1       2.6
3.3       0.6
3.1       8.8
3.7       5.6
0.7       10.3
2.5       6.5
2.3       1.6
5       0.6
0.3       0.8
4.1       7.9
3.4       3.5
6.2       7.5
8       6.5
7.8       3.3
1.8       3.2
0.3       2.4
0.7       3.3
14.1   3.6
5.1       8.1
2.5       3.9
3.3       1
1.5       2
19.5   27.9
3       15.4
1.8       0.5
3       0.5

A marketing manager for Country Kitchen Corporation (CKC), which sells snack food product "Nature -Bar" in dif- ferent regions, was interested in how its sales (denoted Sales) are influenced by the sales of its main competitor (denoted Csales.) She gathered last year data on Sales and Csales for a 15 randomly selected sales regions and ob- tained the regression model of Sales on Csales. Both Sales and Csales are measured in millions of dollars. To answer questions below use your own Minitab output.

The data are in Excel file Nature-Bar.

a) Is the regression of Sales on Csales statistically significant at a= 0.02? (State the hypothesis test, rejection rule and your conclusion)