Introduction 27 and p 0 = 1 - k=1 p k , where 0 < p < 1 and p b p/(1 - p). (a) Evaluate p 0 in terms of b and p. (b) What does the generalized geometric distribution reduce to when b = p? When b = p/(1 - p)? (c) Show that N = X + Z has the generalized geometric distribution when X is a Bernoulli random variable for which Pr{X = 1} = , 0 < < 1, and Z independently has the usual geometric distribution given in (1.25). 1.4 Important Continuous Distributions For future reference, this section catalogs several continuous distributions and some of their properties. 1.4.1 The Normal Distribution