Consider two random variables X and Y with the same range RX = RY = {a1, a2,

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Consider two random variables X and Y with the same range RX = RY = {a1, a2, a3}, and suppose that E(X) = E(Y) and Var(X) = Var(Y).

(i) Prove that E(X2) = E(Y2).

(ii) Show that the quantities xi = P(X = ai) − P(Y = ai), i = 1, 2, 3, satisfy a homogeneous linear system of equations, for which the determinant of the coefficient matrix for the unknowns has the formimage text in transcribed

(iii) Explain why the distributions of the random variables X and Y coincide, i.e.
we have P(X = ai) = P(Y = ai)
for i = 1, 2, 3.

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Introduction To Probability Volume 2

ISBN: 9781118123331

1st Edition

Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis

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