2 BH 414 Let X have PMF PX k cpk k for k 1 2 where p

2. (BH 4.14) Let X have PMF P(X = k) = cpk /k for k = 1, 2, . . . , where p is a parameter with 0 < p < 1 and c is a normalizing constant. We have c = 1/ log(1 p), as seen from the Taylor series log(1 p) = p + p 2 2 + p 3 3 + . . . . This distribution is called the Logarithmic distribution (because of the log in the above Taylor series), and has often been used in ecology. Find the mean and variance of X.

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