Let X have PMF P(X = k) = −p^k/(k log(1 − p)) for k = 1, 2, 3, ...,where p is a parameter such that 0 < p < 1. (Note: the terms LOOK negative, but thatrestriction on p causes the log to be negative, making the fraction positive!) This distributionis called the Logarithmic distribution, often used in ecology. Calculate the expectation of X.
Let X have PMF P(X = k) = −p^k/(k log(1 − p)) for k = 1, 2, 3, ...,where p is a parameter such that 0 < p < 1. (Note: the terms LOOK negative, but thatrestriction on p causes the log to be negative, making the fraction positive!) This distributionis called the Logarithmic distribution, often used in ecology. Calculate the expectation of X.
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 4ECP
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Let X have PMF P(X = k) = −p^k/(k log(1 − p)) for k = 1, 2, 3, ...,
where p is a parameter such that 0 < p < 1. (Note: the terms LOOK negative, but that
restriction on p causes the log to be negative, making the fraction positive!) This distribution
is called the Logarithmic distribution, often used in ecology. Calculate the expectation of X.
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