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Closed form for the moment generating function

Find a closed form for the moment generating function of a discrete uniform random variable, that is, for the random variable X with pmf p(x) = 1/n for x = 1,2,3,....,n.(hint: use lemma 2.6.1.)

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## Q : Number of different binary sequences of length

Count the number of different binary sequences of length 20 that consist of a positive number of zeros, followed by a positive number of ones, followed by a positive number of zeros, followed by a positive number of ones.