You have two sets of corresponding measurements \(X = x_1, x_2, \ldots, x_n\) and \(Y = y_1, y_2, \ldots, y_n\). Their covariance, \(\text{Cov}(X,Y)=12.\) What is the covariance if you double all measurements, i.e. what is \(\text{Cov}(2X,2Y)\)?

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You have a data set with standard deviation 10. What is the minimum value of the standard deviation of the data set obtained by taking the absolute value of all the elements of the original data set?

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Suppose you have data points \(x_1, \ldots, x_n\) with mean 5 and variance 2. If I first multiply them all by three and then square all the new values I get, what is the mean of the data points I end up with?

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