Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Answer questions 7.4.13, 7.4.14 and 7.4.15 respectively

[画像:7.S13 WP A random variable x has probability density function f(x) = 2013 X2 e-x/0 е 0 < x < ∞, 0 < 0 < ∞ Find the maximum likelihood estimator for O. 7.S14 Letf(x) = (1/0)x(1-0)/0,0<x<1, and 0 <0 < ∞o. Show that = (1/n) In(X;) is the maximum likelihood estimator for e and that is an unbiased estimator for q. i=1 7.S15 An electric utility has placed special meters on 10 houses in a subdivision that measures the energy consumed (demand) at each hour of the day. The company is interested in the energy demand at one specific hour-the hour at which the system expe- riences peak consumption. The data from these 10 meters are as follows (in KW): 23.1, 15.6, 17.4, 20.1, 19.8, 26.4, 25.1, 20.5, 21.9, and 28.7. If μ is the true mean peak demand for the 10 houses in this group of houses having the special meters, estimate μ. Now suppose that the utility wants to estimate the demand at the peak hour for all 5000 houses in this subdivision. Let 0 be this quantity. Estimate 0 using the data given. Estimate the proportion of houses in the subdivision that demand at least 20 KW at the hour of system peak.]
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Transcribed Image Text:7.S13 WP A random variable x has probability density function f(x) = 2013 X2 e-x/0 е 0 < x < ∞, 0 < 0 < ∞ Find the maximum likelihood estimator for O. 7.S14 Letf(x) = (1/0)x(1-0)/0,0<x<1, and 0 <0 < ∞o. Show that = (1/n) In(X;) is the maximum likelihood estimator for e and that is an unbiased estimator for q. i=1 7.S15 An electric utility has placed special meters on 10 houses in a subdivision that measures the energy consumed (demand) at each hour of the day. The company is interested in the energy demand at one specific hour-the hour at which the system expe- riences peak consumption. The data from these 10 meters are as follows (in KW): 23.1, 15.6, 17.4, 20.1, 19.8, 26.4, 25.1, 20.5, 21.9, and 28.7. If μ is the true mean peak demand for the 10 houses in this group of houses having the special meters, estimate μ. Now suppose that the utility wants to estimate the demand at the peak hour for all 5000 houses in this subdivision. Let 0 be this quantity. Estimate 0 using the data given. Estimate the proportion of houses in the subdivision that demand at least 20 KW at the hour of system peak.
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