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?
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?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 3P: Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the...
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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?
Transcribed Image Text:Setup the complete pmf first. So, 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).
Here's a part of the pmf table:
www
1
3
O 0.124357822
???
???
???
???
1
???
???
???
???
Y
???
0.020657
0.000918
???
???
???
3
4 5.35547E-05
???
???
???
???
???
???
???
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
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 smile. 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.
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