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Unformatted text preview: function) for the expression in (a). In other words, provide an expression for Pr ( n i =1 X i > x ) using the central limit theorem. c) Compute (a) and (b) for n = 50 , and x = 80 and comment on your answers. Problem 4 Let X i ,i = 1 , 2 ,...,n be n i.i.d. random variables, with M x ( ) = E [ e X ] . a) Show that for any , Pr ( e X e a ) E [ e X ] e a b) Argue that Pr ( X a ) = Pr ( e X e a ) . c) Using (a) and (b), show that Pr ( X > a ) e-[ a-log M X ( )] d) bserve that the bound in (c) is true for ANY . Thus, conclude that Pr ( X > a ) exp(-max [ a-log M X ( )]) (e) Compute the bound for the example in Problem (3) and comment....
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This note was uploaded on 10/26/2009 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas at Austin.
- Spring '07