Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2017 • Question 1

Question

Math 6010 • Linear Models Fall 2017 • Question 1

Let \(X_1,X_2,\ldots ,X_n\) be iid random variables with probability mass function \[ f(t;\theta )=\theta (1-\theta )^{t-1}, \qquad t=1,2,3,\ldots \] Find the uniformly minimum variance unbiased estimator of \(\theta \).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be iid random variables with probability
mass function
\[
  f(t;\theta)=\theta(1-\theta)^{t-1}, \qquad t=1,2,3,\ldots
\]
Find the uniformly minimum variance unbiased estimator of \(\theta\).

Topic Tags

Estimator Distributions Measure-Theoretic Probability Sufficiency, Completeness, and UMVUE Uniform Integrability and Truncation Methods