Suppose that we want to estimate the parameter of the geometric distribution on the basis of

Suppose that we want to estimate the parameter θ of the geometric distribution on the basis of a single observation. If the loss function is given by

And Θ is looked upon as a random variable having the uniform density h(θ) = 1 for 0 < θ < 1 and h(θ) = 0 else-where, duplicate the steps in Example 9.9 to show that 

(a) The conditional density of given X = x is

(b) The Bayes risk is minimized by the decision function d(x) = 2 / x + 2

Transcribed Image Text:

x(x + 1)6(1-θ)"-1 for 0 <θ <1 elsewhere