Please help with all parts of this problem :)

1. Consider the following model and assumptions. Assume that {31 and 52 are xed unknown constants, and that {$1, . . . ,xn} are xed known constants with m, 7E no, for at least some 2' 75 j. K- : [3'1 + [32 exp(93,-) + 61;, 3': 1, - -- ,n, where 6,; 13 N(0, 02). You may assume and use any results you know from P8 TAT 127 or gore-requisite courses to answer this question. (a) Write down the distribution of Y}. Your answer must include the distribution name, and the mean and variance. (b) Are Y1, . . . ,Yn independently and identically distributed (i.e., are they iid)? (Answer Yes or No.) (c) Is this a linear model in the sense of PSTAT 126? Why or why not? (d) Based on your answer to part (1a), write out the likelihood of 60 and [31 based on observations {311, . . . , yn}. Your answer will be a function of [30, 61, y1,. . . ,y,, and x1, . . . ,wn