Two random variables X and Y have a joint PDF fX,Y(X, y) that is equal to...

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Two random variables X and Y have a joint PDF fX,Y(X, y) that is equal to a constant K in the shaded region shown in Figure, and is equal to zero elsewhere. (a) (i) Find K (ii) Make a labeled sketch of the marginal PDF fY(y) (i) Make a labeled sketch of the conditional PDF frx(y ) (b) Find the MMSE estimate of Y given that X x has been observed, i.e., the conditional mean E(YX x) , wherex can be any value between 0 and 2. (c) Find the LMMSE estimate of Y given that X x has been observed, where x can be any value 3 = between 0 and 2. Note that E(YX) for the joint probability density function shown in Figure. fx.y (x.y) 1 0 0 2. N Two random variables X and Y have a joint PDF fX,Y(X, y) that is equal to a constant K in the shaded region shown in Figure, and is equal to zero elsewhere. (a) (i) Find K (ii) Make a labeled sketch of the marginal PDF fY(y) (i) Make a labeled sketch of the conditional PDF frx(y ) (b) Find the MMSE estimate of Y given that X x has been observed, i.e., the conditional mean E(YX x) , wherex can be any value between 0 and 2. (c) Find the LMMSE estimate of Y given that X x has been observed, where x can be any value 3 = between 0 and 2. Note that E(YX) for the joint probability density function shown in Figure. fx.y (x.y) 1 0 0 2. N