Exercise 4.1 The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. a. Suppose that the joint p.m.f of X and Y is modeled as fry (x, y) = c(x+y), x=1, 2, 3 and y=1, 2, 3 Determine the value of c. b. Determine the marginal p.m.f of X. Find also the mean and variance of X. c. Determine the conditional p.m.f of Y given X-2. Find also the conditional mean and conditional variance of Y given X=2. d. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent.

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