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.

Beatrice decides she wants to babysit a few children at the same time to earn the money faster. she tells parents that if they allow her to babysit their children at her house, she will eliminate her automatic $5 tip and will give them an additional $5 discount. (a) write an equation showing the total cost for each client. identify all variables. (b) four parents bring their children to beatrice’s house at the same time for babysitting. beatrice wants to find out how many hours she must babysit the 4 children to earn exactly the $100 she needs in order to buy the present for her mother. write and solve an equation to find the number of hours. justify each step in the solution. (c) one parent decides not to drop off her child. the remaining 3 parents drop their children off at 9 a.m. two of the parents say they will be back at 1 p.m. the third parent says she will pick up her child at 2 p.m. at noon, beatrice realizes she needs feeding the 3 ch

Apatient is given 50 mg dose of medicine the medicines effectiveness decreases every hour at a constant rate of 40% what is the exponential decay function that models this scenario how much medicine will be left in the patients system after 2 hours

Ineed with angles and the measure of them i have abc a is 65 and b is (3x-10) and c is (2x) find the value of x