Your Textbook Suggests Using the First Observation from a Sample

Essay

Your textbook suggests using the first observation from a sample of n as an estimator of
the population mean.It is shown that this estimator is unbiased but has a variance of
σ2 , which makes it less efficient than the sample mean.Explain why this estimator is
Y
not consistent.You develop another estimator, which is the simple average of the first
and last observation in your sample.Show that this estimator is also unbiased and show
that it is more efficient than the estimator which only uses the first observation.Is this
estimator consistent?