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# CSIR NET Mathematics 2024| Estimation | 19 February 2024

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Question 1

A sample of 10 observations for random variable X given by:

0.70, 0.55, 0.31, 0.40, 0.35, 0.62, 0.34, 0.77, 0.45, 0.64

Let X is assumed to follow a continuous uniform distribution within the interval [0, ].

Find the estimate of  using method of moment.

Question 2

Let  be independent and identically distributed continuous uniform variables over the interval [0, ]. If  is the maximum likelihood estimator of  then find the bias of the estimator

Question 3

Let  be a random sample from a population with probability function

Then which of the following is an unbiased estimator of ?

Question 4

For the following probability function:

Obtain the estimator of  by the method of moments, if the frequencies at x = 0,1, 2, and 3 are respectively 27, 22, 20, and 18

Question 5

Let and  is a sample of size 5 from a distribution with probability mass function

Obtain the maximum likelihood estimator of

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