Question: Moments of Function

Hello Please,

 

I was wondering if the moments(mean, variance,...) of this function bellow exists even if in approximate form.

 

f(x) = binomial(x+r-1, x)*((1/2)*b/(1+d*x+(1/2)*b))^r*((d*x+1)/(1+d*x+(1/2)*b))^x/(d*x+1)

 

Somebody, please help.

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