Question

Poisson distribution gives the probability that x events occur in unit time when the mean rate of occurrence is m. 

P_x = (e^−mm^x )/x! 

(a) Show that P_x is normalized. 

(b) Show that the mean rate of occurrence or the expectation value < x >, is equal to m. 

(c) Show that the S.D., σ = √m 

(d) Show that P_m−1 = P_m 

(e) Show that P_x−1 = (x/m)P_m and P_{x + 1} = m/(x + 1)P_x

Answer 1

That is the probability for the occurrence of the event at x = m − 1 is equal to that at x = m