For problem: 4 - 10 , determine whether each is an exponential family with kas small as possible. To fully understand what you are expected to learn here, you must be able to give correct expressions for all parts (four or six) of the answer. For the purpose of grading these problems, you will only be asked to identify the part for the t(x). Here are the choices (A) - (J) for the answers on the online graded homework on problems 4 -- 10. (A) o(x) = log(x) (B) Ox) = log(1-x] (C) t(x) = ex (D) ((x) = ex (E) ((x) = x (F) ((x) = 1/x (G) * where the exponent r here is a number besides 1 or -1. (H) Can be written as an exponential family but requires k > 1, so there two or more expressions for t(x). (!) Can be written in the form of an exponential family with k = 1 but the statistic that is different from any of these and cannot be modified to be one of these by changing the form of the function of the parameter. (Recall the example from the Pareto dist'n in which we modified the form of the function of x.) (J) Not an exponential family (Cannot be written in the form of an exponential family.) 4. Consider a distribution with pdf f (x) =p(1-p)" where x=1, 2, 3, .. and 00 9. Consider a distribution with pdf f (x| 8) =e-(x-?) exp(-e-(x-?) ), -co