A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively. A sample of four pages is selected without replacement, and X and Y denote the number of pages with moderate and high graphics output in the sample, respectively.What is the marginal standard deviation of the number of pages among those chosen with high graphics? NOTES!You need to setup the complete pmf first. So, you have to compute the probabilities for each joint values of X and Y. For example, P(X=1,Y=1) is the chance of selecting 1 page with moderate graphics and 1 page with high graphics and 2 other pages that have low graphics (do not forget that 4 pages are to be selected, and pages can either have low, moderate, or high graphics). Note that you cannot have X=4 and Y=1, because there are only 4 pages to be selected at random. Once you have all the probabilities in the pmf, compute the marginal probabilities of X. (i.e., P(X)P(X)) Compute the marginal mean of Y using the marginal probabilities. Or, there's a quicker way to do this. Since 10% of the 100 pages have high graphics, then that same probability should hold true if you take a sample of 4 pages from 100 . Nevertheless, you need the pmf table to compute the marginal variance. Compute the marginal variance. Do not forget that the 2nd term of the formula is the square of the marginal mean. Do not forget that it's the standard deviation that is being asked here.

From the given information, a small-business web site contains 100 pages and 60%, 30% and 10% of the…

Answered: A small-business Web site contains 100…

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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A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively. A sample of four pages is selected without replacement, and X and Y denote the number of pages with moderate and high graphics output in the sample, respectively.

What is the marginal standard deviation of the number of pages among those chosen with high graphics?

NOTES!

You need to setup the complete pmf first. So, you have to compute the probabilities for each joint values of X and Y. For example, P(X=1,Y=1) is the chance of selecting 1 page with moderate graphics and 1 page with high graphics and 2 other pages that have low graphics (do not forget that 4 pages are to be selected, and pages can either have low, moderate, or high graphics).

Note that you cannot have X=4 and Y=1, because there are only 4 pages to be selected at random.

Once you have all the probabilities in the pmf, compute the marginal probabilities of X. (i.e., P(X)P(X))

Compute the marginal mean of Y using the marginal probabilities. Or, there's a quicker way to do this. Since 10% of the 100 pages have high graphics, then that same probability should hold true if you take a sample of 4 pages from 100 . Nevertheless, you need the pmf table to compute the marginal variance.