Suppose X1, X2, . .. . X, be an iid random sample of size n from a population and it's probability density function given by f(x) = T(a + B) "-1(1 -x)3-1 for 0 0,3>0 (a) (2 points) In statistics, what is sufficiency? Explain in formal mathematical terms, and. in colloquial terms. Answer succinctly and concisely (b) (6 points) Suppose the parameter S is known and can be treated as a constant. Show IIn 1 x; is a sufficient for a. c) (6 points) Suppose the parameter o is known and can be treated as a constant. Show IIt(1 - r;) is a sufficient for B. d) (6 points) Suppose both parameters o and B are equal (a = ), show EL-, In(z,(1 -x;)) is sufficient for the parameter S and a