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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2005 • Question 6

Question

Math 6010 • Linear Models 2005 • Question 6

Let \(X_1,\ldots ,X_n\) be independent, identically distributed random variables with probability mass function \[ f(t,\theta )=\theta (1-\theta )^{t-1}I\{t=1,2,\ldots \}\qquad (0<\theta <1). \] Find the uniformly minimum variance unbiased estimator for \(\theta \).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be independent, identically distributed random variables with probability mass function
\[
f(t,\theta)=\theta(1-\theta)^{t-1}I\{t=1,2,\ldots\}\qquad (0<\theta<1).
\]
Find the uniformly minimum variance unbiased estimator for \(\theta\).

Topic Tags

Covariance and Independence Estimator Distributions Measure-Theoretic Probability Sufficiency, Completeness, and UMVUE