A random vector T = (X, Y)T has the probability density function 0x1 and 0 ...

 

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A random vector T = (X, Y)T has the probability density function 0≤x≤1 and 0 ≤ y ≤ x² otherwise 3 fr(x, y) = {{ 0 where k > 0. (a) Sketch the region on which fr(x, y) is positive. (b) Using a double integral with vertical strips, calculate the expected value E(XY) of XY for this probability distribution. (c) In one or two sentences, explain why the random variables X and Y are NOT independent. A random vector T = (X, Y)T has the probability density function 0≤x≤1 and 0 ≤ y ≤ x² otherwise 3 fr(x, y) = {{ 0 where k > 0. (a) Sketch the region on which fr(x, y) is positive. (b) Using a double integral with vertical strips, calculate the expected value E(XY) of XY for this probability distribution. (c) In one or two sentences, explain why the random variables X and Y are NOT independent.