Question

1. Submit your el 2. The assignment can be done individually or in small groups (2-3 students). 3. The names o assignment electronically through iLearn by the due date: Friday, August 3. fall members of a group must be clearly stated in the work submitted for grading. Only one submission per group, please! 4. The answers to quest tions 1 11 below, including the graphs, must be clearly stated in a single word or pdffile separate from your code or Excel file. Violation to this rule will result in a zero score for all members of the group. The answers must be supported by either a code or Excel file showing all work. If you used Excel, save all your data in Excel file. You may use different tabs for different parts of the assignments. Label your work. 5. 6. 7. If you used any other software, be sure to attach your 8. code and the output. (The output without any code shown will not be given any credit!) Submit the assignment to ILEARN. Follow the links to submit different portions assignment. You may have to submit up to 3 different files: word or pdf, an Excel file, a code and the output (if used a program other than Excel). of the OBJECTIVE: Demonstrate the Central Limit Theorem 1. 2. You will simulate a continuous uniform distribution. The theoretical model you will work with is X-U(0,1). What is the mean and standard deviation of this theoretical model? State the the answer Generate 100,000 of observations th formula and 3. at follow a continuous uniform distribution between 0 and 1. (Do it in such a way that you can think of 100,000 observation as 1,000 samples, each a size of 100.) Report the sample mean and the sample standard deviation of the entire set of 100,000 observations you have generated. Construc Now, compute the sample mean for each sample. You should have 1,000 sample means. (Do not compute 1000 of sample standard deviations.) Construct a histogram of the sample means. (What shape do you see?) Report the mean and the variance of the sample means you generated. With respect to a random variable X, describe its theoretical distribution: the shape, the expected value, and the standard deviation! 4. 5. 6. t a histogram of these 100,000 observations. (What shape do you expect to see?) 7. 8. 9. 10. Use the appropriate theoretical model to compute the probability that the sample mean is within its one standard deviation of the true population mean. 11. What percent of your random samples have the sample mean within one standard deviation of the population mean?

Answer 1