## Jointly Bernoulli Distribution

Let

$x_i \sim \text{Bernoulli}(p_i) : p_i \in [0,1], x_i \in \{ +1, -1\}.$
What is the expression for the joint distribution of the the vector $X = [x_1, x_2, ... , x_N]$.
What is the entropy $h(X)$ of the vector $X$ where

$h(X) = -\sum_{\forall X \in \{+1,-1\}^N} p(X) \log (p(X)).$

 Tags entropy, probability