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13.4 Exercise 4

Avg difficulty 2.5

Simple random variable X has distribution

X = [ - 3 - 2 0 1 4 ] P X = [ 0 . 15 0 . 20 0 . 30 0 . 25 0 . 10 ] X = \left[- 3 - 2 0 1 4\right] P X = \left[0 . 15 0 . 20 0 . 30 0 . 25 0 . 10\right]
  1. Determine the moment generating function for X.
  2. Show by direct calculation the MX'(0)=E[X]M_{X}^{'} \left(0\right) = E \left[X\right] and MX''(0)=E[X2]M_{X}^{' '} \left(0\right) = E \left[X^{2}\right].

Pfeiffer, Applied Probability, 13.4 Problems on Transform Methods, exercise 4

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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.