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 numbe of pages with moderate and high graphics output in the sample, respectively. 1 If the first drawn page has moderate ranhics what is the probability that
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 numbe of pages with moderate and high graphics output in the sample, respectively. 1 If the first drawn page has moderate ranhics what is the probability that
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Please help me answer these three questions. Notes are indicated in the bullets.
![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.
1. If the first drawn page has moderate graphics, what is the probability that
there are no pages with low graphics chosen?
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.
2. If there are no pages with moderate graphics drawn, how many pages with
high graphic content would you expect in the sample? Express your answer
up to three decimal places.
• If it is known (sound's like a condition) that X=1, and if there are no low graphic page selected, then the other
pages
Actually, you do not need the entire table. Your sample space is limited to X=1, so we are only interested with
probabilities of Y given that X=1.
Compute the marginal probability of X=1. (i.e., P(X = 1)).
• Compute the conditional probability being asked. Recall that P(A|B) =
P(ANB)
and
P(B)
P(AN B) = fAB(A, B).
P(AnB)
and
P(B)
Compute the conditional probabilities of Y given X=0. Recall that P(A|B)
P(AN B) = fAB(A, B).
Compute yfy]z=0)
Compute the expected value of Y given x=0.
3. What is the variance of Y given that there are no pages with moderate
graphics drawn? Express your answer up to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28541f55-435c-4c6c-bef4-d2ae84f3b478%2F8ba5d5aa-062d-47cc-8aaf-2c624703b2b8%2F9wzt79q_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
1. If the first drawn page has moderate graphics, what is the probability that
there are no pages with low graphics chosen?
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.
2. If there are no pages with moderate graphics drawn, how many pages with
high graphic content would you expect in the sample? Express your answer
up to three decimal places.
• If it is known (sound's like a condition) that X=1, and if there are no low graphic page selected, then the other
pages
Actually, you do not need the entire table. Your sample space is limited to X=1, so we are only interested with
probabilities of Y given that X=1.
Compute the marginal probability of X=1. (i.e., P(X = 1)).
• Compute the conditional probability being asked. Recall that P(A|B) =
P(ANB)
and
P(B)
P(AN B) = fAB(A, B).
P(AnB)
and
P(B)
Compute the conditional probabilities of Y given X=0. Recall that P(A|B)
P(AN B) = fAB(A, B).
Compute yfy]z=0)
Compute the expected value of Y given x=0.
3. What is the variance of Y given that there are no pages with moderate
graphics drawn? Express your answer up to three decimal places.
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