# Question

Find an example (other than the one given in Example 5.15) of two random variables that are uncorrelated but not independent.

## Answer to relevant Questions

Determine whether or not each of the following pairs of random variables are independent: (a) The random variables described in Exercise 5.6; (b) The random variables described in Exercise 5.7; (c) The random variables ...Two random variables are jointly Gaussian with means of μx = 2, μy = –3, variances of σ2x = 1, σ2y = 4, and a covariance of Cov (X, Y) = –1. (a) Write the form of the joint PDF of these jointly Gaussian random ...A pair of random variables has a joint characteristic function given by Find E [X] and E [Y] Find E [XY] and Cov (X, Y). Find E [X2Y2] and E [XY3]. Let and be jointly Gaussian random variables. Show that Z = aX + bY is also a Gaussian random variable. Hence, any linear transformation of two Gaussian random variables produces a Gaussian random variable. Suppose and are independent, zero- mean Gaussian random variables with variances of σ2x and σ2y respectively. Find the joint PDF of Z = X2 + y2 and W = X2 – Y2Post your question

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