Math 6010 • Linear Models

Let \(X,Y\) be independent random variables with respective densities
\[
  f(t)=
  \begin{cases}
    0, & \text{if } t\notin[-2,3],\\
    \dfrac{1}{5}, & \text{if } t\in[-2,3],
  \end{cases}
\]
and
\[
  g(t)=
  \begin{cases}
    0, & \text{if } t\notin[-1,5],\\
    \dfrac{1}{6}, & \text{if } t\in[-1,5].
  \end{cases}
\]
Compute the density of \(X+Y\).