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Unformatted text preview: variables that are uniformly distributed between [0 , 1] . Using Chebyshevs inequality and assuming x n 2 , a) Provide a bound on Pr ( n i =1 X i > x ) . b) Use the central limit theorem approximation to provide an approximation (in terms of the 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 6 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 ) and that, therefore, Pr ( X a ) e-[ a-log M X ( )] ....
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- Spring '07