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Earn +20 ptsQ: Obtaining moment generating function of poisson distribution?
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Which distribution function has equal mean and variance?
The exponential distribution and the Poisson distribution.
Moment generating and the cumulant generating function of poisson distribution?
The moment generating function is M(t) = Expected value of e^(xt) = SUM[e^(xt)f(x)] and for the Poisson distribution with mean a inf = SUM[e^(xt).a^x.e^(-a)/x!] x=0 inf = e^(-a).SUM[(ae^t)^x/x!] x=0 = e^(-a).e^(ae^t) = e^[a(e^t -1)]
If X has Poisson distribution does aX plus b have Poisson Distribution?
Yes.
Why belong exponential family for poisson distribution or geometric distribution?
Why belong exponential family for poisson distribution
How do you calculate the mean and variance of a poisson distribution as a function of time t?
Divide the total number of incidents by the total time. The result, representing the average number of incidents per unit of time, is the mean as well as the variance of the Poisson distribution.
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