Homeword

Project description
1. Use Excel to simulate the following 2 activities.

Toss a coin 100 times and read its upward facing side. Assign a “1? to a head and a “0? to a tail. Let “X” be the random variable representing the outcome of each

toss. Use 8787 for the random seed. (Due to a flaw in Random Number Generation in Analysis ToolPak of Excel, you may need to select “Normal” in the field,

“Distribution:”, in order to enter the random seed before selecting “Discrete” in the field, “Distribution:”.)

Roll a die 100 times and read its upward facing side. Let “Y” be the random variable representing the number of dots on the upward facing side. Use 3434 for the

random seed. The 2 different random seeds ensure that Excel simulates (1) tossing the coin and (2) rolling the die as independent activities.

Let W = X + Y.

Set up your Excel spreadsheet in such a way that you can do part (e) by merely updating the simulated outcomes for the 2nd activity: rolling the die 100 times.

(a) Calculate the sample mean and the sample variance of the 100 values for X. Calculate the population mean (µX) and the population variance (sX2) and compare

them to the sample mean and the sample variance, respectively.

(b) Calculate the sample mean and the sample variance of the 100 values for Y. Calculate the population mean (µY) and the population variance (sY2) and compare

them to the sample mean and the sample variance, respectively.

(c) Calculate the sample mean and the sample variance of the 100 values for W. Calculate the population mean (µW) and the population variance (sW2) and compare

them to the sample mean and the sample variance, respectively. To calculate the population variance (sW2), use the equation in part (d) with ? = 0.

(d) Use the sample variances to estimate the value of the correlation coefficient, ?, in the following equation.

sW2 = sX2 + sY2 + 2?sXsY

Is the value (of ?) that you estimated reasonable?

(e) In the previous parts of this exercise, you used different random seeds in order to simulate the independence of the 2 activities. Redo the previous 4 parts (of

this exercise) by using the same random seed, 8787, for both activities. Using the same random seed causes the simulated outcomes of the 2 activities to be

dependent. When you calculate the population variance (sW2) in part (c), use ? = 1.

Homework 5 is due at the beginning of class on October 15.

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Please heed the following instructions.

A. For your homework submission, briefly explain the formulas that you used in Excel to do the homework. Do not print all the data.

B. After you finish your homework, use a staple to attach all its pages of paper.

C. The homework submission must be a physical document that you give to the instructor. Do not e-mail the homework submission to the instructor.