Question

Multi-part question:

Let X1, .... ,Xn be random variables that describe the accumulated rainfall per
month.

A) Write the statistical model (there might be more than one suitable statistical model.)

B) Assume that the random variables that describe the accumulated rainfall per month have the
following p.d.f.

a_1 _주

Find the moment estimators of a and θ (you can use the results from the table of distributions).

C) Under the assumptions in (B) and assuming that a is known, find the maximum likelihood estimator
of θ.

D) Under the assumptions in (b) and assuming that a = 1, find the maximum likelihood estimator
of the median accumulated rainfall per month.

(Note: recall that if xmed is the median of a positive random variable X, then xmed is such that

)

E) Under the assumptions in (b) and assuming that a = 1, show that the maximum likelihood
estimator of θ forms a consistent sequence of estimators for θ.

Answer 1