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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2005 • Question 7

Question

Math 6010 • Linear Models 2005 • Question 7

Let \(X\) and \(Y\) be independent random variables with densities, \[ g(t)= \begin {cases} 0, & \text {if } t\notin [-2,2],\\ 1/4, & \text {if } t\in [-2,2], \end {cases} \] and \[ f(t)= \begin {cases} 0, & \text {if } t\notin [-1,1],\\ 1/2, & \text {if } t\in [-1,1]. \end {cases} \] Compute the density of \(X+Y\).

Raw LaTeX

Let \(X\) and \(Y\) be independent random variables with densities,
\[
g(t)=
\begin{cases}
0, & \text{if } t\notin [-2,2],\\
1/4, & \text{if } t\in [-2,2],
\end{cases}
\]
and
\[
f(t)=
\begin{cases}
0, & \text{if } t\notin [-1,1],\\
1/2, & \text{if } t\in [-1,1].
\end{cases}
\]
Compute the density of \(X+Y\).

Topic Tags

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