Multiplication excess noise
= Multiplication excess noise
{title2=$F$}
Random multiplication increases the noise relative to deterministic gain. If the output from one input electron has mean $g$ and variance $g^2$, a <Poisson distribution> of input electrons with mean $\mu$ produces output variance $2g^2\mu$, by the <law of total variance>. The high-gain analog-mode excess-noise factor is $\sqrt2$.