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1. A zero-mean Gaussian random signal has the autocorrelation function of the form γX(τ) = 10e-0.1|τ| cos 2πτ.
Write the covariance matrix for the signal sampled at four time instants separated by 0.5 seconds.
2. Find the joint p.d.f. of the signal from Exercise 8.5.1 at t1 = 1 and t2 = 2.5. Write the integral formula for P(0 ≤ X(1) ≤ 1, 0 ≤ X(2.5) ≤ 2). Evaluate the above probability numerically.
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From Data Set VI in Appendix B, select a sample of 20 values and find the 90% confidence interval or the mean of the number of acres. Find the mean of all values, and determine if the confidence interval contains the mean.
The joint cumulative distribution function for (X, Y) is given by F(x, y) = ( 1 - e-x/ID - e-y/l + e-lx+SyJ/I0)/10,001 (x)I10,oodY).
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