MATH 111 Midterm: MATH111 South Carolina Practice Exam 1
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Ground rules: the maximum points of this exam is 100, print your name at the top of this page in the upper right hand corner, this is a closed-book and closed-notes exam. Honor pledge for this exam: after you have nished the exam, please read the following statement and sign your name below it. 1: suppose that x as a beta( , ) distribution. The pdf of x is fx (x| , ) = x 1(1 x) 1i(0 < x < 1). (a) show that {fx (x| , ); > 0, > 0} is a two-parameter exponential family. Also nd e(y ) for > 1. 1 x (c) prove that the mgf of y does not exist. 2: in general, if we say w n (a, b2), then the pdf of w is fw (w) = Now let x n ( , 2) and y n ( , 2).
