Kindly provide accurate solutions

Y1, Y2, .... Y,, are independent claims, which are assumed to be exponentially distributed, with E[YA - Hi - (1) Show that the canonical link function is the inverse link function. [3] (ii) It is decided that the canonical link function should not be used. but that the mean claim sizes should be modelled as follows: logy; = a i=12 ....m P i=m+1, m +2. . ..n (a) Show that the log-likelihood can be written as -mut (n - m) B+e"> >te BE > (b) Derive the maximum likelihood estimators of o and F. (c) Show that the scaled deviance for this model is E vi 2 `log log [12] (iii) For a particular data set, m = 20, n = 44, _ y; = 142. - > y, = 18.7. 44 204 24 * 21 Calculate the deviance residual for y, = 7. [3] [Total 18]