CSIR NET Mathematics 2024| Estimation | 26 April 2024

Let X₁, X₂ be a random sample from a distribution with the probability mass function

f(x|θ) = 1 – θ if x = 0

         =  θ  if x = 1

where 0 < θ < 1

which of the following is not an unbiased estimator of θ ?

Let X₁, X₂ …… X_n, X_n+1 be a random sample from a N(μ, 1) population.

If  and T =

then for estimating μ

Find the efficient estimator of μ.

Let X₁,X₂ ….., X_n as iid from . Find the complete sufficient statistics for

Let . Find the complete sufficient statistics for ?