Master convergence concepts and asymptotic behavior
Let ξₙ →d ξ (convergence in distribution) and ηₙ →P c (convergence in probability to constant c). Wh...
Let ξₙ ~ B(n, 0.1) and lim(n→∞) n × 0.1 = λ > 0. Then ξₙ converges in distribution to:
Which statement about the relationship between almost sure convergence and convergence in probabilit...
Let {ξₙ} be independent and identically distributed random variables with E(ξ₁) = 2 and Var(ξ₁) = 4....
Let ξₙ ~ P(n) (Poisson distribution). When n → ∞, (ξₙ - n)/√n converges in distribution to:
Which condition ensures {ξₙ} satisfies the weak law of large numbers according to Chebyshev?
Let ξₙ →a.s. ξ (almost sure convergence). Which conclusion is INCORRECT?
Using the de Moivre-Laplace theorem to approximate a binomial distribution with n=100, p=0.5, what i...
If Fₙ ⇒ F (weak convergence of distribution functions), which function g(x) guarantees ∫g(x)dFₙ(x) →...
Let {ξₙ} be i.i.d. with E(ξ₁) = μ and Var(ξ₁) = σ² > 0. Then (∑ᵢ₌₁ⁿ ξᵢ - nμ)/(√n σ) converges in dis...