SOLVED: Problem One: Consider a random vector with two components, X and Y. Denote the cumulative distribution function (CDF) Fxy(z, y), and the marginal CDFs as Fx(z) and Fy(y), respectively:i) Show, using first principles, that Fx(z) Fy(y) - 1 < Fxy(z, y) < √(Fx(z) * Fy(y)) always holds.ii) Suppose that X and Y are components of a continuous random vector with a density fx,y(z, y) = c * ry, 0 < y < ∞, 0 < z < 2, and zero elsewhere. Here, c is a normalizing constant.a) Show that c = 1/2.b
SOLVED: Problem One: Consider a random vector with two compone…
1 mai 2023
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