STA215: Statistical Inference

Homework #2

Due: Wednesday, Feb 23

1. Let X_j be a sequence of independent Ga(4,lam) random variables (see explanation of parameterization here), with pdf f(x)=(lam⁴ x³ /6)e^-lam*x for x>0. Then:
   1. Find the MLE T_n(X) for lam, upon observing X₁,...,X_n.
   2. Is T_n(X) consistent? Show that it is.
   3. Set R(T_n,lam) = E[(T_n(X)-lam)² | lam]; Find the limit as n increases of n·R(T_n,lam).
   4. Find an exact 90% (Frequentist) confidence interval for lam, given the n=3 observations X₁=7.2, X₂=3.4, X₃=1.4.

2. Bickel & Doksum problems from pages 142-152: 2.2.10
3. Bickel & Doksum problems from pages 152-154: 2.3.7, 2.3.8
4. Bickel & Doksum problems from pages 197-199: 3.2.1, 3.2.4