Time Left - 25:00 mins
CSIR NET Mathematics 2024| Estimation | 19 February 2024
Attempt now to get your rank among 6 students!
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
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/170789003364837.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890034429728.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890035186645.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890035974884.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890036766618.png)
Question 3
Let
be a random sample from a population with probability function
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890048346416.png)
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
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890067119186.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ123200/1707890067904638.png)
Obtain the maximum likelihood estimator of
- 6 attempts
- 0 upvotes
- 0 comments
Feb 19CSIR NET & SET