# Function x gengaussmunigman 4 the file prog1datmat on

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function X = gengauss(mu,Nigma,N) 4. The file prog1dat.mat (on the class website) contains N 1000 data points representing measurements x 1 , x 2 , x 3 , x 4 from a four-dimensional physical system. Load the data into Matlab using the command load prog1dat A 4 1000 variable X will be created with the data in it. Suppose that x 1 5 and x 3 7 is measured. Determine the best estimate of the variables x 2 and x 4 . Explicitly state all the appropriate covariance and mean vectors, and how you obtain your estimates. 5. Continuing the previous problem,suppose that the variables x 1 , x 2 , and x 3 are available. Write a function predictx4 which will estimate the corresponding value of x 4 . The function should have the “declaration” 2

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function x4hat = predictx4(x1,x2,x3) (with possibly some other arguments as well). If x 1 3, x 2 3 . 6, x 3 5 . 2, what is the estimate of x 4 ? 6. Continuing the previous problem, let X ( 1 ) be obtained from the first two components of the four-dimensional data. Estimate 6 11 , the covariance matrix of X ( 1 ) , and μ ( 1 ) , the mean vector. Plot contours of the pdf of X ( 1 ) . The function plotellipse.m (on the class website) may be helpful. Compare the axes of the ellipses with the eigenvectors of 6 11 . What is the relationship? 3
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