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E(g(X)) = X∞ k=−∞ eskp(k) in the discrete rv case It is so called because it generates the moments of X by differentiation at s = 0 M0(0) = E(X), (7) 2 and more generally M(n)(0) = E(), n ≥ 1 (8) The mgf uniquely determines a distribution in that no two distributions can have the same1 other equivalence classes of size one But these correspond to elements g with gp = eG Since f(e;e;e;;e)g is an equivalence class of size 1, conclude from (f) that there must be a nonidentity element g 2 G with gp = e (show p j k) Since p j jGj and p j pd then pjk We already have (e;e;;e) 2 X so k is at least one, thus k is at least p Thus there are at least p ¡ Applied Sciences Free Full Text A Nonlinear Beamformer Based On P Th Root Compression Application To Plane Wave Ultrasound Imaging Html ƒ‚ƒ"ƒXƒg ƒEƒŠƒGƒ‹ ƒKƒ`ƒƒ