Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2015 • Question 9

Question

Math 6010 • Linear Models Fall 2015 • Question 9

Let \(X_1,X_2,\ldots ,X_n\) be independent and identically distributed random variables with density function \[ f(t)= \begin {cases} 0, & \text {if } t<0,\\ \dfrac {1}{\lambda }\exp (-t/\lambda ), & \text {if } t\geq 0. \end {cases} \] Construct an equal tail \(1-\alpha \) confidence interval for \(\lambda \). Compute the expected value of the length of the confidence interval.

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent and identically distributed
random variables with density function
\[
f(t)=
\begin{cases}
0, & \text{if } t<0,\\
\dfrac{1}{\lambda}\exp(-t/\lambda), & \text{if } t\geq0.
\end{cases}
\]
Construct an equal tail \(1-\alpha\) confidence interval for \(\lambda\). Compute
the expected value of the length of the confidence interval.

Topic Tags

Covariance and Independence Measure-Theoretic Probability Simultaneous Confidence Intervals Uniform Integrability and Truncation Methods