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Let X(t) be a Gaussian process with mean µX (t) and autocovariance CX(t,τ). In this problem, we verify that the for two samples X(t1), X(t2), the multivariate Gaussian density reduces to the bivariate Gaussian PDF. In the following steps, let σ2i denote the variance of X(ti) and let ρ = CX (t1,t2 - t1)/(σ1σ2) equal the correlation coefficient of X(t1) and X(t2).
(a) Find the covariance matrix C and show that the determinant is
(b) Show that the inverse of the correlation matrix is
(c) Now show that the multivariate Gaussian density for X(t1), X(t2) is the bivariate Gaussian density.
(a) What is the average number of customers in the shop? (b) What is the proportion of potential customers that enter the shop? (c) If the barber could work twice as fast, how much more business would he do?
Describe in your own words the difference between a means objective and a fundamental objective. Why do we focus on coming up with attribute scales that measure accomplishment of fundamental objectives, but not means objectives? What good does it ..
If you draw one ball from the urn what is the probability that it is blue or white?
(a) Find an expression which serves as a linear approximation for l at h=1000 m. (b) Give two assumptions you think have been made in deriving the expression above.
patient waiting times in the tardis orthopedic clinic have a mean of 50 minutes with a standard deviation of 25
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For the sample of men, performance on the simulator task declined by an average of 2.9 points with s = 4.1. Is this a statistically significant change? Use a two-tailed test with = .05.
Make an argument about the effects of nation-building - both in the Andersonian sense of "imagining" a national community and in the Weberian sense of modernization and integration - on European history during the long 19th century.
1.a sample of 50 male and 50 female infants were put on an experimental infant formula. after two weeks the parents of
We have no idea Regarding the shape of the population distribution. What is the probability that the mean fee for a sample of 30 customers was less than $125?
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