8. The quantum noise in x-ray imaging obeys Poisson distribution: NK e-N PK K! where: P is probability, in a given time interval, of emitting K photons from an x-ray source, N is the average number of photons emitted during that interval, and K! is the factorial of non-negative integer. Please prove that in Poisson process, the variance is given as: o² = N. Hint: the following may be helpful: o² = Σ(K-N)² x PK K=0 K=0 K²xPx = N² +N co N = KXPK K=0
8. The quantum noise in x-ray imaging obeys Poisson distribution: NK e-N PK K! where: P is probability, in a given time interval, of emitting K photons from an x-ray source, N is the average number of photons emitted during that interval, and K! is the factorial of non-negative integer. Please prove that in Poisson process, the variance is given as: o² = N. Hint: the following may be helpful: o² = Σ(K-N)² x PK K=0 K=0 K²xPx = N² +N co N = KXPK K=0
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Transcribed Image Text:8. The quantum noise in x-ray imaging obeys Poisson distribution:
NK e-N
PK
K!
where: P is probability, in a given time interval, of emitting K photons from
an x-ray source, N is the average number of photons emitted during that
interval, and K! is the factorial of non-negative integer.
Please prove that in Poisson process, the variance is given as: o² = N.
Hint: the following may be helpful:
o² = Σ(K-N)² x PK
K=0
ΣΚ K²xPx = N² +N
K=0
co
N = KXPK
K=0
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