We now introduce a poisson intensity parameter λt for every time point and denote the parameter ( ) that gives the canonical exponential family representation as above by θ . we choose to employ a linear model connecting the time points t with the canonical parameter θ of the poisson distribution above, i. e., θ=a+ in other words, we choose a generalized linear model with poisson distribution and its canonical link function. that also means that conditioned on t , we assume the yt to be independent. imagine we observe the following data: t1=1 1 outbreaks t2=2 3 outbreakst3=4 10 outbreaks 1. we want to produce a maximum likelihood estimator for . to this end, write down the log likelihood of the model for the provided three observations at t1 , t2 , and t3 (plug in their values).2. what is its gradient? enter your answer as a pair of derivatives.