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 random variable X has a logarithmic series distribution with parameter p if (a) Verify that this defines a legitimate probability functi...

a x1 1p x x log p 1log p x1 1p x x 1 since the sum is th ...

Starting from the O-truncated negative binomial (refer to Exercise 3.13), if we let r 0, we get

Question:

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.)

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...