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

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SUMMARY

The discussion centers on the moment generating function (MGF) and its relationship with the first raw moment. It establishes that the first raw moment about zero is derived from the first derivative of the MGF evaluated at t=0. The confusion arises from the integration of the function etxfx(x)dx, which is necessary to obtain the MGF before differentiating it. The integration process is crucial as it transforms the function into a form that allows for the extraction of moments through differentiation.

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RufusDawes
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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 ?
 
Physics news on Phys.org
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.
 

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