The position and elevation of a survey station are given by the random vector x= x, in |X3 which X, and X2 are the planimetric coordinates, and X3 the elevation. The standard deviations are 0.020 m, 0.045 m, and 0.025 m respectively. Correlation coefficient between X, and X2 is -0.50. There is no correlation between X, and X, or between X, and X3. 4.1. Evaluate the covariance-variance matrix, Ex.

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The position and elevation of a survey station are given by the random vector
x=X,
in
which X, and X2 are the planimetric coordinates, and X3 the elevation. The standard deviations
are 0.020 m, 0.045 m, and 0.025 m respectively. Correlation coefficient between X, and X2 is
-0.50. There is no correlation between X, and X3, or between X2 and X3.
4.1. Evaluate the covariance-variance matrix, E.
4.2. Evaluate the weight matrix, W, if the reference variance chosen is 0.000625 m?.
Transcribed Image Text:The position and elevation of a survey station are given by the random vector x=X, in which X, and X2 are the planimetric coordinates, and X3 the elevation. The standard deviations are 0.020 m, 0.045 m, and 0.025 m respectively. Correlation coefficient between X, and X2 is -0.50. There is no correlation between X, and X3, or between X2 and X3. 4.1. Evaluate the covariance-variance matrix, E. 4.2. Evaluate the weight matrix, W, if the reference variance chosen is 0.000625 m?.
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