Probability

[luca.barletta]

Consider a set of $n$ independent Bernoulli variables ${c_1,...,c_n}$ (i.e. $c_i in {0,1}$)
with a priori probabilities defined by $lambda_i=log((P(c_i=1))/(P(c_i=0)))$.
Let $Phi=sum_(i=1)^n c_i$ denote the modulo-2 summation of ${c_i}$; show that the a priori
probability $lambda_Phi$ of $Phi$ obeys to the following:

$lambda_Phi=-2arctanh(prod_(i=1)^n tanh(-lambda_i/2))$