Exercise 1.6. Zero Inflated Poisson. Let x_(1), ..., x_(n) be a random sample from the Poisson (位) distribution but truncated on the left at 0, that is, the sample space of each x_(i) is {1, 2, ...} and P(x_(i) = x) = (1)/(1 - e^(-位)) * (位^(x)e^(-位))/(x!), x = 1, 2, ... Please show the UMVUE of (位)/(1 - e^(-位)) attained the Cram茅r-Rao lower bound.
Exercise 1.6. Zero Inflated Poisson. Let X1, ..., Xn be a random sample from the Poisson() distribution but truncated on the left at 0, that is, the sample space of each Xi is {1, 2, ...} and P(Xi = x) = 1 - e^(-x)/(x!), x = 1, 2, ...
Please show the UMVUE of X/(1 - e^(-位)) attained the Cram茅r-Rao lower bound.