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13.4 Exercise 11

Avg difficulty 2.5

Random variable X has moment generating function

M X ( s ) = 1 1 - 3 s ⋅ exp ( 16 s 2 / 2 + 3 s ) M_{X} \left(s\right) = \frac{1}{1 - 3 s} \cdot \exp \left(16 s^{2} / 2 + 3 s\right)

By recognizing forms and using rules of combinations, determine E[X]E \left[X\right] and Var [X]Var \left[X\right].

Pfeiffer, Applied Probability, 13.4 Problems on Transform Methods, exercise 11

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.