Poisson

你問0的題目好難(仲難過上次個條)﹐你唔比答案我都未必諗到
poisson distribution
(λ^x)(e^-λ)/x!
E[X] = In 2
λ=ln2
the poisson distribution becomes
1/2[(ln2^x)/x!]
E[cos(πX)]
=1/2Σcos(πx)[(ln2^x)/x!] [x from 0 to infinity]
=1/2[1-ln2+(ln2)^2/2!-(ln2)^3/3!+...-...]
=1/2(e^-ln2)
=1/2*1/2
=1/4