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Ngày đăng: 21/01/2014, 06:20
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Tài liệu tham khảo | Loại | Chi tiết |
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2.1 Derive a rule for computing the values of the cdf of the single variable gaussian (2.4) from the known tabulated values of the error function (2.5) | Khác | |
2.7 Assume that x 1 and x 2 are zero-mean, correlated random variables. Any orthogonal transformation of x 1 and x 2 can be represented in the formy | Khác | |
2.8 Consider the joint probability density of the random vectors x = (x 1 x2 )Tand y = y discussed in Example 2.6:pxy( x y ) =((x1 + 3x2 )y x1 x22 0 1] y 2 0 1]0 elsewhere | Khác | |
2.8.1. Compute the marginal distributions p x( x ) , p y ( y ) , p x1 (x 1 ) , and p x2 (x 2 ) | Khác | |
2.8.2. Verify that the claims made on the independence of x 1 , x 2 , and y in Example 2.6 hold | Khác | |
2.9 Which conditions should the elements of the matrixR = a c d bsatisfy so that R could be a valid autocorrelation matrix of 2.9.1. A two-dimensional random vector | Khác | |
2.10 Show that correlation and covariance matrices satisfy the relationships (2.26) and (2.32) | Khác | |
2.11 Work out Example 2.5 for the covariance matrix C x of x , showing that similar results are obtained. Are the assumptions required the same | Khác | |
2.12 Assume that the inverse R 1 x of the correlation matrix of the n -dimensional column random vector x exists. Show thatE f x T R 1 x x g = n | Khác | |
2.13 Consider a two-dimensional gaussian random vector x with mean vector m x= (2 1) T and covariance matrixC x = 1 2 1 2 | Khác | |
2.13.2. Draw a contour plot of the gaussian density similar to Figure 2.7 | Khác | |
2.14 Repeat the previous problem for a gaussian random vector x that has the mean vector m x = (2 3) T and covariance matrixC x = 2 2 2 5 | Khác | |
2.15 Assume that random variables x and y are linear combinations of two uncor- related gaussian random variables u and v , defined byx = 3u 4v | Khác |
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