Answer Happy

Question 14. ♣ = μlį and Let X₁, X2, ··· be a sequence of independent random variables, with E[X;] Var(X₂) = o?, for i = 1, 2, . . . . Suppose that 0 < o? < M, for all i. Let a be an arbitrary positive number. One can affirm that: None of these answers are correct n 1 P ( 2-¹ TX - 2 - ¹ ¹ Ë H₂ | > a) < Var (X₁) ++ Var(Xn) 0 n 2n²a² i=1 n P (|X, - - ±¹ | > a) < Var(X1) + ... +* Var(Xn) n n²a² i=1 P ( 2X - 2²/1¹4² > 2ª) · 2a Var (X₁) + ... + Var(X₂) n²a² n P ( X - 1 2 H | > a) Xn Hi ≤2· Var(X₁) + ··· + Var(X₂) n² a² Question 15. ♣ We keep the notations of Question 14. From the result of Question 14, one can conclude that: n 1 None of these answers are correct lim P n→∞ (|X₁ - ² E 14 | > a) € R n Hi n n 1 lim P P ( X ₁ - ² 2 μ | > a) = ₁ n Hi 0. n i=1 1 (|X₁ - ² Σ µ₁ | > a) Xn Hi does not exist. n 0 n→∞ lim P n→∞