Repeat the previous exercise for the following prior (again, a form of beta density):

\[p(r)=\left\{\begin{array}{cc} 3 r^{2} & 0 \leq r \leq 1 \\ 0 & \text { otherwise } \end{array}\right.\]

What are the prior parameters here?

Data from previous exercise

Repeat the previous exercise for the following prior, also a particular form of the beta density:

\[p(r)=\left\{\begin{array}{cl} 2 r & 0 \leq r \leq 1 \\ 0 & \text { otherwise } \end{array}\right.\]

What are the values of the prior parameters \(\alpha\) and \(\beta\) that result in \(p(r)=2 r\) ?