Using excel with formulars

for binomial random variable X with n=10, p=0.3, plot its pdf and cdf; then simulate from it a sample of size N=2000, plot its histogram (relative frequency), and cumulative frequency.

For a sex-linked gene at which there are two alleles, A1 and A2, in a population and for which the frequency of A1 is 0.9 in females and 0.3 in males, what will be the frequency of the A1 allele in the male offspring (sons) after one generation of random mating?

1. Which of the following statements correctly describes the short-term response towards a reduction in wealth.

   		The FE curve stays unchanged
   		The FE curve shifts to the right
   		The FE curve shifts to the left
   		None of the above

0.3 points   

QUESTION 10

1. Which of the following statements correctly describes the short-turn response towards an increase in current output

   		The IS curve stays unchanged
   		The IS curve shifts to the right
   		The IS curve shifts to the left
   		None of the above

0.3 points   

QUESTION 11

1. Which of the following statements correctly describes the short-turn response towards a decrease in lump-sum taxes, assuming that households are myopia and do not expect the future tax increase.

   		The IS curve stays unchanged
   		The IS curve shifts to the right
   		The IS curve shifts to the left
   		None of the above

1. The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.

a.  Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter.

b. Compare the three-period moving average forecast with the exponential smoothing forecast using α = 0.3. Which appears to provide the better forecast based on MSE?

A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.

(a)Test the hypotheses H0: p = 0.3 versus H1: p ≠ 0.3 with α = 0.05, using the normal approximation.

(b)Find the P-value for this test.

(c)Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used to test the hypothesis in part (a).

(d)Using the point estimate of p obtained from the preliminary sample of 50 helmets, how many helmets must be tested to be 95% confident in order to keep the associated β-error at 0.1 (or the power at 90%)?

3) The very first magnetic resonance imaging (MRI) devices employed multi-layer copper solenoids, like the one shown in the figure below. The solenoid dimensions were: length = 2 m and inner radius = 0.4 m. The required magnetic field was 0.3 T. Due to thermal considerations, the copper wire conductor was chosen to have a square cross-section, 10 mm×10 mm, which limited the maximum current in the conductor to 1,000 A.

A) What is the minimum number of solenoid layers needed to achieve the required magnetic field? Assume that the conductor in each layer is tightly wound on a cylinder, without any gaps.

B) For the chosen number of layers and using the copper resistivity value at room temperature, estimate the electrical power consumption of this solenoid at 0.3 T.

A professor has constructed a 3-by-4 two-dimensional array of float numbers. This array currently contains the lab grades, quiz grades and exam grades of three students in the professor’s class. Write a C++ program that calculate the final grade for each student and save it to the last column. You program should display the following output:             Lab    Quiz      Exam       Final    

Student 1          ## ## ## ##

Student 2          ## ## ## ##

Student 3          ## ## ## ##

The final grade consists of 30% lab grade, 30% quiz grade and 40% exam. For example, if lab grade is 95, quiz grade is 82 and exam grade is 87, the final grade is equal to 95∗0.3+82∗0.3+87∗0.4. Use random numbers between 40 and 100 for lab, quiz and exam grades.

1. ) Suppose a stock had an initial price of $37 per share, paid a dividend of $0.3 per share during the year, and had an ending share price of $50. Compute the percentage total return. Enter the answer in 4 decimals.

2. ) Calculate the arithmetic average of the following returns.

Year Return

1 0.18

2 0.08

3   0.11

4   -0.05

5 0.3

Enter the answer with 4 decimals.

3.) Calculate the standard deviation of the following returns.

Year Return

1 -0.18

2 -0.06

3   -0.09

4   0.21

5 0.08

Enter the answer with 4 decimals.

4. ) Calculate the variance of the following returns.

Year Return

1 -0.16

2 0.08

3   -0.08

4   0.14

5 -0.02

Enter the answer with 4 decimals.

An R-C circuit with R = 100 ohm and C = 3 mF is connected to a 90 V source of emf. At t = 0 the switch is closed and the capacitor begins to charge.

a) How much energy (in J) is stored in the capacitor at t = 0.7 s?

b) What is the largest amount of energy that can be store in the capacitor?

You are trying to build the small scale hydroelectric power plant on the hill. Potential energy is the main energy that you can use to generate the electricity. How much of the water (in kg) should be in the source to provide the 7 kW of power to the house? Assume that the efficiency of the electricity generator is 0.7 and g=9.8 m/s2 .