Question: 23. Let X be a discrete random variable with probability mass function p(i) = 6 2i2 , i = 1, 2, 3,... ; zero elsewhere.

23. Let X be a discrete random variable with probability mass function p(i) = 6 π2i2 , i = 1, 2, 3,... ; zero elsewhere. Show that the moment-generating function of X does not exist. Hint: Show that MX(t) is a divergent series on (0,∞). This implies that on no interval of the form (−δ, δ), δ > 0, MX(t) exists.

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To show that the momentgenerating function MGF of X does not exist we evaluate MXt mathbbEetX sumi1i... View full answer

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