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### Homework10

Course: ST 561, Fall 2010
School: Oregon State University
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Word Count: 117

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2010 Homework ST561 Fall 10 Due: Wed, Dec. 8th, 2010 1. Let Xj , j = 1, 2, 3 are independent with Xj having a gamma distribution with parameter j and 1. Let Y1 = X2 X1 , Y2 = , Y3 = X1 + X2 + X3 . X1 + X2 + X3 X1 + X2 + X3 Find the joint distribution of (Y1 , Y2 , Y3 ). Are the transformed variables independent? 2. Let X1 and X2 be independent, with X1 an having Exp(1) distribution and X2 a Uniform(0,1)...

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2010 Homework ST561 Fall 10 Due: Wed, Dec. 8th, 2010 1. Let Xj , j = 1, 2, 3 are independent with Xj having a gamma distribution with parameter j and 1. Let Y1 = X2 X1 , Y2 = , Y3 = X1 + X2 + X3 . X1 + X2 + X3 X1 + X2 + X3 Find the joint distribution of (Y1 , Y2 , Y3 ). Are the transformed variables independent? 2. Let X1 and X2 be independent, with X1 an having Exp(1) distribution and X2 a Uniform(0,1) distribution. Find the p.d.f. of Y = X1 + X2 . 3. Let X have a t-distribution with p degrees of freedom. Show that X 2 has a Fdistribution with 1 and p degrees of freedom. 4. Let S 2 be the sample variance of a random sample of size 6 from a N (, 12) distribution. Find P (2.30 < S 2 < 22.2). 1
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Oregon State University - ST - 561
ST561Fall 2010Homework 9Due: Monday, Nov. 29th, 20101. Let X = (X1 , . . . , Xp )T follow a multivariate normal distribution with mean and covariance matrix . That is X M V N (, ) with joint pdf fX (x) = 1 (2 )p/2 |1/2 exp (x )T 1 (x )/2where | is th
Oregon State University - ST - 561
ST561Fall 2010Homework 8Due: Monday, Nov. 22th, 20101. Let X1 and X2 be independent Uniform(0,1) random variables. Find the distribution of X2 /X1 . 2. Suppose X has pdf fX (x) for &lt; x &lt; . Express fY (y ) in terms of fX (x) for the following transform
Oregon State University - ST - 561
ST561Fall 2010Homework 7Due: Monday, Nov. 15th, 20101. Suppose X is a real valued random variable such that P (X &gt; 0) = 1 and E (X ) &lt; . Show that Cov (X, 1/X ) &lt; 0. 2. Let X 1 and X 2 be the sample means of two independent samples of size n from the
Oregon State University - ST - 561
ST561Fall 2010Homework 6Due: Monday, Nov. 8th, 20101. Consider any two random variables X1 and X2 with V (X1 ) = V (X2 ) &lt; . Let Y1 = X1 + X2 and Y2 = X1 X2 . (a) Show that Cov (Y1 , Y2 ) = 0. (b) Use the result in (a) to construct a pair of random va
Oregon State University - ST - 561
ST561Fall 2010Homework 5Due: Monday, Nov. 1th, 20102 2 1. Suppose X1 and X2 are independent N (0, 1) random variables. Find P (X1 + X2 1).2. Textbook Page 164, 3.4.2. 3. Textbook Page 167, 3.5.12. 4. Textbook Page 168, 3.5.13.2 5. Let X1 and X2 be i
Oregon State University - ST - 561
ST561Fall 2010Homework 4Due: Monday, Oct. 25th, 20101. Choose a point at random from the interval (0, 1) and call this random variable X1 . If x1 is the observed value of X1 , choose a point at random from the interval (0, x1 ) and call this random va
Oregon State University - ST - 561
ST561Fall 2010Homework 3Due: Monday, Oct. 18th, 20101. Text Page 57, 1.6.3 2. Let f (x) be a p.d.f and let a be a number such that, for all &gt; 0, f (a + ) = f (a ). Such a p.d.f. is said to be symmetric about the point a. Show that if a random variable
Oregon State University - ST - 561
ST561Fall 2010Homework 2Due: Friday, Oct. 8th, 2010 1. (From Homework 1) Four cards are drawn from a deck of 52, without replacement. (a) What is the probability that all 4 cards are aces? (b) What is the probability of drawing, in order, the aces of c
Oregon State University - ST - 561
ST561Fall 2010Homework 1Due: Monday, Oct. 4th, 2010 Note: The rst 4 exercises below are not to be handed in. Please make sure you can do them (and ask about them if you have questions). 1. Find the union A1 A2 and intersection A1 A2 of two sets A1 and
Oregon State University - ECE - 468
Oregon State University - ST - 561
ST561: Study problems for Quiz #41. Let Y1 and Y2 have joint density function fY1 ,Y2 (y1 , y2 ) = 8y1 y2 , 0 &lt; y1 &lt; y2 &lt; 1. and U1 = Y1 /Y2 and U2 = Y2 . Derive the joint density of (U1 , U2 ). Show that U1 and U2 are independent. 2. Let X follow a gamm
Oregon State University - ST - 561
ST561: Study problems for Quiz #31. Let X have a Uniform(0,1) distribution. (a) Use Chebyshevs inequality to nd a bound for P (|X 1/2| 0.35). (b) Find the exact of P (|X 1/2| 0.35). (c) Find the p.d.f. of Y = eX . (Be sure to specify the support of Y ).
Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - ST - 561
Oregon State University - CS - 325
CS 325 Due: Fri 3 DecHomework #9 The Knights Tour ProblemA knight is a chesspiece which can legally move from a square (i, j ) on a chessboard (where i is the row index, and j is the column index) to any of the eight squares (i 1, j 2), (i 1, j + 2), (i
Oregon State University - CS - 325
Oregon State University - CS - 325
CS 325 Due: Friday 19 NovHomework #7 Searching in WonderlandIn Wonderland, there are n n chessboards. For each such chessboard there are n queens each of whom sits proudly on her square so that when she looks down her row, her column, or her diagonals s
Oregon State University - CS - 325
Oregon State University - CS - 325
Oregon State University - CS - 325
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Oregon State University - CS - 325
Oregon State University - CS - 325
Oregon State University - CS - 325
Oregon State University - CS - 325
Oregon State University - CS - 321
Homework 7 CS 321 Due Date: 12/3/10, 2 PM Note: The homeworks should be your own work. You can discuss the homeworks orally with your peers, however. You should not use any web sources for this assignment. Please see the TA and the instructor during the o
Oregon State University - CS - 321
Oregon State University - CS - 321
Homework 5 CS 321 Due Date: 11/10/10, 2 PM Note: The homeworks should be your own work. You can discuss the homeworks orally with your peers, however. You should not use any web sources for this assignment. Please see the TA and the instructor during the
Oregon State University - CS - 321
Oregon State University - CS - 321
Oregon State University - CS - 321
Oregon State University - CS - 321
Homework 1 CS 321 Due Date: 10/6/10, 2 PM Note: The homeworks should be your own work. You can discuss the homeworks orally with your peers, however. You are allowed to use the internet sources only when you are explicitly asked to do so. In such cases, y
Oregon State University - ECE - 468
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Oregon State University - ECE - 468
ECE 468: Digital Image Processing Lecture 24Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu1Outline Color models (Textbook 6.2) Color transformations (Textbook 6.5)2Visible Spectrum of EM3Based on Psychophysical StudiesCones in the human eye
Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
ECE 468: Digital Image Processing Lecture 21Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu1Outline Wavelet functions (Textbook 7.2.3) Wavelet transform in 1D (Textbook 7.3)2Wavelet Function Spaces3Scaling FunctionsGiven:(x)j,k (x) = 2j/2
Oregon State University - ECE - 468
ECE 468: Digital Image Processing Lecture 21Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu1OutlineExam 2 review2OutlineMultiresolution expansions (Textbook 7.2)3
Oregon State University - ECE - 468
ECE 468: Digital Image Processing Lecture 20Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu1OutlineExam 22Next ClassExam 2 review3
Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
ECE 468: Digital Image Processing Lecture 11Prof. Sinisa Todorovic sinisa@eecs.oregonstate.eduOutline Homework 3 Preparation for Exam 1Next ClassExam 1
Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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Oregon State University - ECE - 468
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UC Irvine - CHINESE - 100
.H n Hn h O S * *. . Z* , I.. . , 4 * iD , . ,H n Yucyuyfjizhudxudt.Zijizhu,yushsujizhudxuxioyun.Ksh,jizhudxu jijnshnfnxiozhyuylioxuxio,miyubnk.Dngrn,wmenduzhdojizhudxu lushnjfnxioshzuhodejizhudxu.H n* SATII,H n * .H n . ,. SATACT Hn .H n .. * 3
Colorado Christian - CSL - 653
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T HOMSONB ROOKS/COLE*Linear Algebra and Its Applications, Fourth Edition Gilbert StrangAcquisitions Editor: John-Paul Ramin Assistant Editor: Katherine Brayton Editorial Assistant: Leata Holloway Marketing Manager: Tom Ziolkowski Marketing Assistant:
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