Homework Help is Here – Start Your Trial Now!
Math
Probability
Question 4. 4(a) Let X1,..., X be iid random variables from a Binomial distribution with n=4 and p-0.1. Let X=}EX. Find the exact value of P(X < 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).

Question 4. 4(a) Let X1,..., X be iid random variables from a Binomial distribution with n=4 and p-0.1. Let X=}EX. Find the exact value of P(X < 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).

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...
See similar textbooks
icon
Related questions
Question

this is one wholle question pls help no half anwsers pls

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:
For which values of p, k, and n do you expect the histograms to be closer to a normal distribution? Your comments/answer: 4(c)(ii) Use your simulate data to approximate P(X <np) that you found in part 4(a). Report your approximated values in three 3-by-3 tables, with the first table corresponding to p-0.1, the second table corresponding to p-0.25, and the third one for p=0.5 (in each table, the rows represent the values of k and the columns are the values of n). You must attach a copy of your 'R' codes for each part (so that I can run them to reproduce similar results).
Transcribed Image Text:For which values of p, k, and n do you expect the histograms to be closer to a normal distribution? Your comments/answer: 4(c)(ii) Use your simulate data to approximate P(X <np) that you found in part 4(a). Report your approximated values in three 3-by-3 tables, with the first table corresponding to p-0.1, the second table corresponding to p-0.25, and the third one for p=0.5 (in each table, the rows represent the values of k and the columns are the values of n). You must attach a copy of your 'R' codes for each part (so that I can run them to reproduce similar results).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Inequality
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS