exam1s99

# exam1s99 - STAT 501 Spring 1999 EXAM I NAME _ Instructions:...

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STAT 501 EXAM I NAME __________________ Spring 1999 Instructions: You may use only your calculator and the attached tables and formula sheet. You can detach the tables and formula sheet from the rest of this exam. Show your formulas and answers in the space provided on this exam. Credit will be given for exhibiting a correct method or correct formulas, even when the final numerical answer is missing or incorrect. If you need more room use the back of the page or attach extra sheets of paper, but clearly indicate where this is done. Put your name on any pages you attach to this exam. 1. Suppose X = (X 1 , X 2 , X 3 , X 4 )' has a multivariate normal distribution with mean vector and covariance matrix m = 4 2 - 3 - 1 S = 97 35 - 7 - 14 - 35 - 78 12 24 7 - 12 22 4 14 - 24 4 28 The eigenvalues for Σ are λ 1 = 132, λ 2 = 55, λ 3 = 20 and λ 4 . (a) What is the distribution of + + - 3 2 1 4 1 3 2 X X X X X ? (b) What is the value of the smallest eigenvalue λ 4 ? (c) Is a =  - 0 , 0 , 5 2 , 5 1 an eigenvector for Σ ? Explain.

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2 (d) What is the conditional distribution of X 1 and X 3 given that 4 2 X X = - 4 2 ? (e) What is the partial correlation between X 1 and X 3 given X 2 = - 1 and X 4 = 3 ? (f) List properties of | Σ | that make it a reasonable measure of dispersion for X = (X 1 , X 2 , X 3 , X 4 )' . 2. A manufacturer of electrical components buys electrodes from two suppliers named supplier 1 and supplier 2. In a quality control study of these suppliers, n 1 = 20 electrodes were randomly selected from those purchased from supplier 1 and n 2 = 80 electrodes were randomly selected from those selected from supplier 2. Three measurements were made on each electrode:
3 These measurements, shown in the diagram, are all made in units of 10

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## This note was uploaded on 12/16/2011 for the course STAT 5705 taught by Professor Staff during the Fall '09 term at FSU.

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exam1s99 - STAT 501 Spring 1999 EXAM I NAME _ Instructions:...

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