CSIR NET Mathematics 2024| Estimation | 15 April 2024

Given the observations 0.8, 0.71, 0.9, 1 .2, 1 .68, 1 .4, 0.88, 1 .62 from the uniforms distribution on

(θ – 0.2, θ + 0.8) with – ∞ < θ < ∞

Which of the following is a maximum likelihood estimate for θ?

Suppose X₁, X₂, …., X_n is a random sample from a population X with density function

f(x) =  0 < x < θ

find an estimator of θ by method of moment?

A sample of size 10 having observations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is taken from N(θ, 1). Find MME of θ?

Let X₁, X₂, ……, X_n be the random sample from a population X with Exp (θ).

Find the MLE of Pr(X > 10) = ?

Let X₁, X₂ …….. X_n be a random sample from a bernoulli population with parameter P. Find the sufficient statistics for P.