## “Intensity” channels

Consider a random variable x taking discrete values $$x \in \{x_1,x_2,\ldots,x_n\},$$ with probability mass function $$p(x_i).$$ If all the possible values of x are positive, it turns out that the following is also a valid probability mass function (all positive, sums to 1): $$q(x_i) = p(x_i) \frac{x_i}{E[X]},$$ where $$E[X] = \sum_i x_i p(x_i)$$ is the expected value of x. … [Read more…]