[Solved] The logarithmic series model was introduced by R.A. Fisher to study the distribution of butterflies on the Malayan Peninsula and has been used
Question: The logarithmic series model was introduced by R.A. Fisher to study the distribution of butterflies on the Malayan Peninsula and has been used in various biological, demographic and economic applications. The model is
\[p(x \mid \theta)=\left(\frac{1}{x}\right)\left(\frac{\theta^{x}}{-\log (1-\theta)}\right), x=1,2, \ldots ; 0<\theta<1\]Show that the logarithmic series model is an exponential family. Use Theorem $1.6 .2$ to find the moment generating function of the logarithmic series \((\theta)\) distribution and calculate the mean and variance of a random variable \(X\) logarithmic series \((\theta)\) distribution
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![[Solved] If r=5 inches and θ=.5 radian](/images/solutions/MC-solution-library-52965.jpg "[Solved] If r=5 inches and θ=.5 radian find the arc")
[Solved] If r=5 inches and θ=.5 radian find the arc
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