If the moment generation function is the integral of e^tx.fx(x).dx

[RufusDawes]

from zero to infinity,

and the first raw moment about zero is the first derivative of the mgf evaluated at t=0... then why do we need to integrate the function ?

Wouldn't the first raw moment just be e^tx.fx(x) dx, i.e the derivative of the function we just integrated ?

Why do we integrate and then find the derivative of the same function ?

 

[Stephen Tashi]

No. You aren't paying attention to which variable is used in the integration and which variable is used in the differentiation. Look at some specific examples.