On page 12-13 of chapter 13 it puts the pdf of normal distribution into the form of f(y; theta, phi) = exp[(ytheta - b(theta)) / a(phi) + c(y, phi)] however I am confused how it goes from the pdf into this form. How would you know that c(y, phi) = -1/2 (y^2/sigma^2 + log2*pi*sigma^2) ?
Theta is a function of the mean of the distribution. Phi is the "other" parameter - in this case, sigma. Hence, the c(y,phi) function should only have y's and phi's (ie sigmas) in it. And yes, you should absolutely be able to reparameterise these for the exams.
