Nelder & Wedderburn 1972 - Generalized Linear Model - The Random Componet - Equation 1

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In this video I will discuss equation 1 in the famous paper by Nelder & Wedderbur, 1972. In particular, I will show that the expected value of first derivative of the log-liklihood is zero.
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Could you show that alpha, zeta, g, h and Beta have exponential distribution on video?

lenmorales