bim251h2

bim251h2 - = BIM 251 Medical Image Analysis Homework#2 Due...

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===================================================================== BIM 251 Medical Image Analysis Winter 2009 ===================================================================== Homework #2 Due February 2 1. Random vector generation and transformation a) Let f be a random vector composed of three independent identically distributed (i.i.d.) normal random variables with zero mean and unit variance. Find a linear transformation g Af b =+ such that g has its mean and covariance matrix given by 43 1 {, 3 9 1 11 1 }2 31 g g EK = ⎡⎤ ⎢⎥ = ⎣⎦ . b) Find a unitary matrix Φ such that the covariance matrix of yg = Φ is diagonal. c) Find the mean, covariance, and PDF of y . (You can use MATLAB for all the calculations.) 2. Write a MATLAB program to verify your results in problem 1a using Monte Carlo simulation. a) generate N=100 samples of f using function ‘randn’. Calculate g using the transformations you find in problem 1a. Calculate the sample mean and covariance of g . b) Are your sample mean and covariance EXACTLY equal to the mean and covariance given in problem 1a?

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bim251h2 - = BIM 251 Medical Image Analysis Homework#2 Due...

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