Two measurements method are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurement of each of the two methods. a). Suppose that the joint p.d.f. of X and Y is modeled by fxy(x,y) =c, 0

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Two measurements method are used to evaluate the surface smoothness of a paper product. Let X and Y denote the measurement of each of the two methods.

a). Suppose that the joint p.d.f. of X and Y is modeled by fxy(x,y) =c, 0<x<4,0<y and x-1<y<x | 1. Determine the value of c.

b). Determine the marginal probability distribution of X. Find also the mean and variance of X.

c). Determine the conditional probability distribution of Y given X-2. Find also the conditional mean and conditional variance of Y given X=2.

d.) Check if the measurements of the two methods X and Y are independent.

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