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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2015 • Question 10

Question

Math 6010 • Linear Models Fall 2015 • Question 10

Let \(X_1,X_2,\ldots ,X_n\) be independent and identically distributed random variables with density function \[ f(t)= \begin {cases} 0, & \text {if } t<0,\\ \dfrac {1}{\lambda }\exp (-t/\lambda ), & \text {if } t\geq 0. \end {cases} \] Find the uniformly minimum variance unbiased estimator for \(\theta =1/\lambda \).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent and identically distributed
random variables with density function
\[
f(t)=
\begin{cases}
0, & \text{if } t<0,\\
\dfrac{1}{\lambda}\exp(-t/\lambda), & \text{if } t\geq0.
\end{cases}
\]
Find the uniformly minimum variance unbiased estimator for
\(\theta=1/\lambda\).

Topic Tags

Covariance and Independence Estimator Distributions Sufficiency, Completeness, and UMVUE Uniform Integrability and Truncation Methods