Let \(X\) be binomial with parameters \(n\), which is constant, and  \(\Theta\) which is  distributed  uniformly on \( (0,1)\).

1. Find \(\mathbf{E}(s^X | \Theta)\)  for any \(s\).
2. Show that for any \(s\)
   \[ \mathbf{E} ( s^X) = \frac{1}{n+1} \big(\frac{1-s^{n+1}}{1-s} \big)\]
   use this to conclude that \(X\) is distributed uniformly on the set \(\{0,1,2, \cdots, n\}\)