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4(b) Repeat Part 4(a) above, once with p30.25 and another time with p-0.50.

4(b) Repeat Part 4(a) above, once with p30.25 and another time with p-0.50.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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part 4b

Question 4. 4(a) Let X1,...,Xx be iid random variables from a Binomial distribution with n=4 and p=0.1. Let X = E X,. Find the exact value of P(X S np) for the following values of k: 10, 50, 100. Repeat this with n=50 and then n=100. Tabulate your results in a well-labeled 3-by-3 table, where the rows represent the values of k, the columns having the values of n, and the cells of the table having the corresponding probabilities. To get points, make sure to show your work clearly (as to how you arrived at your answers). 4(b) Repeat Part 4(a) above, once with p=0.25 and another time with p3D0.50. 4(c) (Approrimation via the Central Limit Theorem (CLT)1 Refer back to the setup of Parts 4(a) and 4(b), and generate N =10000 values of X for each set of value of k, n, and p. (You don't need to report your actual 10000 values of X). 4(c)(i) Obtain the histograms of these 27 sets of simulated valu. You can (and should) have 9 plots per page: The following command tells 'R' to put 9 plots on each page: par (mfrow=c(3,3)). Submit your well-labeled plots; you should have 3 pages of plots with 9 per page (see the R examples posted on Canvass). For which values of p, k, and n are the corresponding histograms closer to a normal (bell-shaped) distribution? Comment: Your comments/answer:
Transcribed Image Text:Question 4. 4(a) Let X1,...,Xx be iid random variables from a Binomial distribution with n=4 and p=0.1. Let X = E X,. Find the exact value of P(X S np) for the following values of k: 10, 50, 100. Repeat this with n=50 and then n=100. Tabulate your results in a well-labeled 3-by-3 table, where the rows represent the values of k, the columns having the values of n, and the cells of the table having the corresponding probabilities. To get points, make sure to show your work clearly (as to how you arrived at your answers). 4(b) Repeat Part 4(a) above, once with p=0.25 and another time with p3D0.50. 4(c) (Approrimation via the Central Limit Theorem (CLT)1 Refer back to the setup of Parts 4(a) and 4(b), and generate N =10000 values of X for each set of value of k, n, and p. (You don't need to report your actual 10000 values of X). 4(c)(i) Obtain the histograms of these 27 sets of simulated valu. You can (and should) have 9 plots per page: The following command tells 'R' to put 9 plots on each page: par (mfrow=c(3,3)). Submit your well-labeled plots; you should have 3 pages of plots with 9 per page (see the R examples posted on Canvass). For which values of p, k, and n are the corresponding histograms closer to a normal (bell-shaped) distribution? Comment: Your comments/answer:
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