Proof: If X1 and X2 are independent, then E[(X1-μ1) (X2-μ2)] = 0.

Question

Question

Proof:

If X₁ and X₂ are independent, then E[(X₁-μ₁) (X₂-μ₂)] = 0.

math Statistics-And-Probability

Answer 1

Answer #1

If X₁ and X₂ are independent,

E(X1X2) E(X1) E(X2) , by definition ...equation(i)

Now,

EX1)X2 -A2)

EX1 X2-1X2 -2X 12

E(X1 X2)- 1E(X2) - 2E(X1)4142 , since $\mu_1$ and $\mu_2$ are constants and we know E(constant) = constant

E(X1X2)-4221 t+ 2

E(X1X2) - 412

E(X1 X2)- E(* E(X2)

Answer 2

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