Exercício 26. Seja \left(X_{1}, X_{2}\right) \sim \operatorname{Trinomial}\left(n, \pi_{1}, \pi_{2}\right), em que p\left(x_{1}, x_{2} \mid \pi_{1}, \pi_{2}\right)=\frac{n!}{x_{1}!x_{2}!\left(n-x_{1}-x_{2}\right)!} \pi_{1}^{x_{1}} \pi_{2}^{x_{2}}\left(1-\pi_{1}-\pi_{2}\right)^{n-x_{1}-x_{2}} \mathbb{1}_{\{0,1, \ldots, n\}}\left(x_{1}\right) \mathbb{1}_{\left\{0,1, \ldots, n-x_{1}\right\}}\left(x_{2}\right).
Mostre que a priori não informativa de Jeffreys para ( \pi_{1}, \pi_{2} ) será