2.2. Let Y1, Y2, ..., Y, denote independent and identically distributed random variables from a power family distribution with parameters a and 0 = 3. Then, as in Exercise 9.43, if a > 0, J ay-/3", 0

5. Suppose Y₁, Y2,..., Y are independent random variables whose density is for y0 for some > 0. (a) Show that the MLE for is f(y) = 30y²e-04³ n ÔMLE = ΣΤ (b) Use the R code to estimate the bias and the variance when n = 20 and 0 = 2.

Suppose Y₁,..., Yn are independent random variables each with the Pareto distribution and E(Y) = (Bo + B1Xi) Is this a generalized linear model with a canonical link? Give reasons for your answer.

Suppose that X₁ = 1; X₂ = 1; X3 = 0; X₁ = 1; X5 = 1, X6 = 1; X₂ = 0; X = 1; X9 = 0, X10 = 0, represents a random sample. Each of these X's comes from the same population and has a density of fx₁ = 0¹-* (1 - 0)*; x = 0,1 First determine the form of the maximum likelihood estimator for 0, then use the MLE formula and the data provided to find an estimate for 0. Round your answer to 3 decimal places. (Answer is 0.4)