Suppose that the random variables Y1,...,Y„{n> 2) satisfy Y; = Bz, + 6. i=1,2,...,, where 1,..., , are iid N(0, o), and both B and o are unknown. (a) Assume z1,...,, are fixed known constants. Here we observe Y = n,,Y = , and the observed data Y = y = (yn,...Yn). Find a two-dimensional sufficient statistic of Y = (Y1,-.,Ym) for (B,0²). (b) Assume now that z1,...,I are random variables with a known joint distribution m(1,...,I), and the z's are independent of q's (it is traditional in the linear regression to use lower case for independent variables z,'s). In this case, the observed data (Y,x) = {(Yi, Ti)}i=1,n. Find a three- dimensional sufficient statistic of (Y,x) for (8,0²).

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