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Question 2. Consider a p-dimensional response variable j, containing p variables, with n observation vectors j1,..., n. The sample mean vector of these observation vectors is denoted by = (1/n) -1 F. Consider a linear combination v of the observation vector j, defined as v = a1y1 + a2y2 + .+ apyp = d'j where aT = (a1, a2, . . . , ap). i) Show that the mean of v is v = a

Question 2. Consider a p-dimensional response variable j, containing p variables, with n observation vectors j1,..., n. The sample mean vector of these observation vectors is denoted by = (1/n) -1 F. Consider a linear combination v of the observation vector j, defined as v = a1y1 + a2y2 + .+ apyp = d'j where aT = (a1, a2, . . . , ap). i) Show that the mean of v is v = a

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question 2. Consider a p-dimensional response variable j, containing p variables, with n observation vectors j1,.., Tn. The sample mean vector of these observation vectors is denoted by j = (1/n) Ji. Consider a linear combination v of the observation vector j, defined as v = a1y1 + a2Y2 + + ap Yp = where äT = (a1, a2, . .., ap). i) Show that the mean of v is ī = aTj ii) Using the results of the previous question and given that E, (vi – 0)² n - 1 show that s? = aT Sa where S is the sample covariance matrix of the random vector j. [Hint: Try writing all the v variables in terms of the corresponding vectors j.]
Transcribed Image Text:Question 2. Consider a p-dimensional response variable j, containing p variables, with n observation vectors j1,.., Tn. The sample mean vector of these observation vectors is denoted by j = (1/n) Ji. Consider a linear combination v of the observation vector j, defined as v = a1y1 + a2Y2 + + ap Yp = where äT = (a1, a2, . .., ap). i) Show that the mean of v is ī = aTj ii) Using the results of the previous question and given that E, (vi – 0)² n - 1 show that s? = aT Sa where S is the sample covariance matrix of the random vector j. [Hint: Try writing all the v variables in terms of the corresponding vectors j.]
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