How do you take the derivative of the function that defines the ...

[Melanie]

According to the books that I have seen, the Poisson random variable is defined to be lamba to the x times e to the minus x, all that over x factorial. I know how to take the derivative of lamba to the x, and I know how to take the derivative of e to the minus x, but how do  you take the derivative of x factorial?
What is the derivative of the function that defines the Poisson random variable?

[Jesse_J]

Does not compute, as some people say.  My book says the Poisson distribution is defined by

f(x; lambda) = lambda^x e^(-lambda) / x!

Moreover, x is an integer, so you can't really take the continuous derivative with respect to x.  You could approximate something like it, by taking the 3 points at x-1, x, and x+1, and fitting a polynomial to it.

Perhaps better would be to have a generalization of the Poisson distribution for continuous event numbers k. This can be achieved by replacing the factorial by the gamma-function, G(k + 1).

[Melanie]

Thanks