Let theta be the unknown market share that a company has for its primary product. Uncertainty in theta is represented by a probability density function of the beta distributional form with a = 54 and b = 46. You have developed the posterior distribution for theta after observing that 64 out of a random sample of 90 customers used the product. %3D Which statement is correct? O A. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, but this discrepancy has not affected the mean of the posterior distribution. O B. In the sample, the proportion of people who used the product is less than the expected proportion based on the prior, and has led to the posterior distribution having a mean smaller than the prior mean but greater then the sample mean. O C. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to the posterior distribution having a mean smaller than the prior mean but less than the sample mean. O D. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to the posterior distribution having a mean greater than the prior mean but less then the sample mean.
Let theta be the unknown market share that a company has for its primary product. Uncertainty in theta is represented by a probability density function of the beta distributional form with a = 54 and b = 46. You have developed the posterior distribution for theta after observing that 64 out of a random sample of 90 customers used the product. %3D Which statement is correct? O A. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, but this discrepancy has not affected the mean of the posterior distribution. O B. In the sample, the proportion of people who used the product is less than the expected proportion based on the prior, and has led to the posterior distribution having a mean smaller than the prior mean but greater then the sample mean. O C. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to the posterior distribution having a mean smaller than the prior mean but less than the sample mean. O D. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to the posterior distribution having a mean greater than the prior mean but less then the sample mean.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Let theta be the unknown market share that a company has for its primary product. Uncertainty in theta is represented by a probability density
function of the beta distributional form with a = 54 and b = 46. You have developed the posterior distribution for theta after observing that 64
out of a random sample of 90 customers used the product.
Which statement is correct?
O A. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, but this
discrepancy has not affected the mean of the posterior distribution.
B. In the sample, the proportion of people who used the product is less than the expected proportion based on the prior, and has led to the
posterior distribution having a mean smaller than the prior mean but greater then the sample mean.
O C. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to
the posterior distribution having a mean smaller than the prior mean but less than the sample mean.
O D. In the sample, the proportion of people who used the product is greater than the expected proportion based on the prior, and has led to
the posterior distribution having a mean greater than the prior mean but less then the sample mean.
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