AI Tutor
Back to 13.4 Problems on Transform Methods

13.4 Exercise 9

Avg difficulty 2.5

Random variable X has moment generating function p2(1-qes)2\frac{p^{2}}{\left(1 - q e^{s}\right)^{2}}.

  1. Use derivatives to determine E[X]E \left[X\right] and Var [X]Var \left[X\right].
  2. Recognize the distribution from the form and compare E[X]E \left[X\right] and Var [X]Var \left[X\right] with the result of part (a).

Pfeiffer, Applied Probability, 13.4 Problems on Transform Methods, exercise 9

AI Tutor

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