# Question: Let X1 X2 Xn be a

Let X1, X2, . . . , Xn be a random sample of size n from the uniform population given by

Show that if Y1 and Yn are the first and nth order statistic, any estimator Θ such that

Can serve as a maximum likelihood estimator of θ. This shows that maximum likelihood estimators need not be unique.

Show that if Y1 and Yn are the first and nth order statistic, any estimator Θ such that

Can serve as a maximum likelihood estimator of θ. This shows that maximum likelihood estimators need not be unique.

**View Solution:**## Answer to relevant Questions

With reference to Exercise 10.72, check whether the following estimators are maximum likelihood estimators of θ: (a) 1/2 (Y1 + Yn); (b) 1/3 (Y1 + 2Y2). In exercise Let X1, X2, . . . , Xn be a random sample of size n from ...With reference to Example 10.3, find an unbiased estimator of d based on the smallest sample value (that is, on the first order statistic, Y1). Example 10.3 If X1, X2, . . . , Xn constitute a random sample from the ...In a random sample of the teachers in a large school district, their annual salaries were $ 23,900, $ 21,500, $ 26,400, $ 24,800, $ 33,600, $ 24,500, $ 29,200, $ 36,200, $ 22,400, $ 21,500, $ 28,300, $ 26,800, $ 31,400, $ ...A history professor is making up a final examination that is to be given to a very large group of students. His feelings about the average grade that they should get is expressed subjectively by a normal distribution with ...If x1 and x2 are the values of a random sample of size 2 from a population having a uniform density with α = 0 and β = θ, find k so that Is a (1 – α) 100% confidence interval for θ when (a) α ≤ 1/2; (b) α > 1/2.Post your question