1a. All maximum likelihood estimators are asymptotically normal.

Question

True
False
b. )
Let X1…Xn be i.i.d. Bernoulli random variables with some unknown parameter . Then which of the following is/are valid confidence interval(s) for with nonasymptotic confidence level 95%?
(Choose all that apply.)

• [[Xn]-1.96(p(1-p)/n)^1/2/n , Xn+1.96(p(1-p)/n)]
•(0,1)
•[0,Xn+.83/n]
•None of above

c.) Which of the following is/are valid statistical model(s)?
•(R,{N(θ,1) θ>10)
•(θ,inf) {t->e^θ-t*1(t>θ)}
•(0,inf), {N(σ, μ)
•(0,inf), {x->e^θx*1(x>0) θ>0}

Answer 1

1. True
2. 1
3. a,b