Question: Starting from the O-truncated negative binomial (refer to Exercise 3.13), if we let r 0, we get an interesting distribution, the logarithmic series distribution. A

Starting from the O-truncated negative binomial (refer to Exercise 3.13), if we let r †’ 0, we get an interesting the logarithmic series A random variable X has a logarithmic series with parameter p if

(a) Verify that this defines a legitimate probability function.
(b) Find the mean and variance of X. (The logarithmic series distribution has proved useful in modeling species abundance. See Stuart and Ord 1987 for a more detailed discussion of this distribution.)

=1,2, 0

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