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Generating function for a random variable

The moment generating function for a random variable X is given by Mx(t) = (1/4)+ (3/4)*(1/(1-t)), t>1. Determine formulas for the density function and distribution function. Sketch graphs for fx and Fx.

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## Q : Confidence interval for the fraction of votes

Of the first 10,000 votes cast in an election, 5180 were for Candidate A. Find a 95% confidence interval for the fraction of votes that Candidate A will receive?