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SOLVED:Mean and variance of an avalanche photodiode probability mass function Starting with the characteristic function Cm(ω) for the output distribution of an avalanche photodiode given by (7.6.3) and repeated here, Cm(ω)=((Ws F)/((F-1)^2)(1-√(1-2 i ωG(F-1)))-i ω(Ws G)/(F-1)), and using (2.2.17), show that the mean of the probability mass function is equal to Es=Ws G, and that the variance is given by σm^2=G^2 Ws(F+Ws)-(Ws G)^2=Ws G^2 F=Es G F .
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