a = > Problem 9 (10 pts) Consider a unit square with four vertices in a two-dimensional Euclidean space, i.e., {(x1, x2)

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A Problem 9 10 Pts Consider A Unit Square With Four Vertices In A Two Dimensional Euclidean Space I E X1 X2 1 (91.56 KiB) Viewed 104 times

a = > Problem 9 (10 pts) Consider a unit square with four vertices in a two-dimensional Euclidean space, i.e., {(x1, x2)|Xi € [0, 1], i = 1,2} . Choose two points P,Q uniformly at random inside the square. Let d?(X,Y) denote the squared distance between the points X and Y. (A) What is E[d(P,Q)]? (B) Suppose that the unit-square is in an n-dimensional Euclidean space, i.e., {(x1,...,xn)|xi € [0, 1], Vi}. What is E[d2(P,Q)]? (C) Apply the Central Limit Theorem and let n goes to infinity. What is the limiting distribution of taldP,EP)? (d?(P,Q) – E[d?(P,Q)])?