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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2010 • Question 5

Question

Math 6010 • Linear Models Spring 2010 • Question 5

Let \(X\) and \(Y\) be two independent random variables with density functions \[ f(t)= \begin {cases} 0, & \text {if } t\notin [0,4],\\ 1/4, & \text {if } 0\leq t\leq 4, \end {cases} \] and \[ h(t)= \begin {cases} 0, & \text {if } -\infty <t<0,\\ 2e^{-2t}, & \text {if } 0\leq t<\infty . \end {cases} \] Compute the density of \(X-Y\).

Raw LaTeX

Let \(X\) and \(Y\) be two independent random variables with density
functions
\[
f(t)=
\begin{cases}
0, & \text{if } t\notin[0,4],\\
1/4, & \text{if } 0\leq t\leq4,
\end{cases}
\]
and
\[
h(t)=
\begin{cases}
0, & \text{if } -\infty<t<0,\\
2e^{-2t}, & \text{if } 0\leq t<\infty.
\end{cases}
\]
Compute the density of \(X-Y\).

Topic Tags

Covariance and Independence Measure-Theoretic Probability Uniform Integrability and Truncation Methods