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Exercise 6.B.3. Let the pair of random variables (X, Y) have joint density function f(x, y)-16(x-y)2 įf x, y e [0, 11, 0 otherwise. a. Confirm that f is a joint density function by verifying that equation (6.B.4) holds, and use a computer or graphing calculator to sketch its graph. b. Compute the marginal density function of Y c. For each x e [0,1], compute the conditional density of Y given x. d. Compute the conditional expectation function E(Y|X = x), and use a computer or graphing calculator to sketch its graph. e. As increases, the areas under the vertical cross sections f(x,) go from being concentrated on high values of y to being concentrated on low values of y. Explain why this seems to contradict your answer to part (d). Then explain why there is actually no contradiction. (Hint: Sketch the graph of fx.)

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Exercise 6.B.3. Let the pair of random variables (X, Y) have joint density function f(x, y)-16(x-y)2...
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