6. X and Y are RVs with a bivariate Gaussian joint density function with means Mx = 4y = 0 and variances o = of = 1. (a)

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6 X And Y Are Rvs With A Bivariate Gaussian Joint Density Function With Means Mx 4y 0 And Variances O Of 1 A 1 (55.38 KiB) Viewed 41 times

6. X and Y are RVs with a bivariate Gaussian joint density function with means Mx = 4y = 0 and variances o = of = 1. (a) If X and Y are independent, find Pr {Y > X>0} (either without a calculation, by considering the area of integration and the shape of the density function or by using an integrator). (b) Suppose X and Y are not independent but positively correlated (p > 0). Without calculating Pr {Y > X>0} for this case, would it be larger than, smaller than, or equal to the answer to section (a)? Hint: Consider the contour plots of the joint Gaussian distributions. (c*) Same as (b) for negatively correlated (p < 0) Gaussian RVs.