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CSIR NET Mathematics 2024| Sampling distribution | 12 April 2024
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Question 1
Let x and y be independent distributed central chi-squared random variables with degree of freedom
and
respectively
![](https://gradeup-question-images.grdp.co/liveData/PROJ105869/1654756946359691.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ105869/1654756947065473.png)
If and m+n = 14
Then is equal to
Question 2
If X ∼ N(0, 1) and X1, X2 is random sample of sie two from the population X, then what is the 75th percentile of the statistics
?
![](https://gradeup-question-images.grdp.co/liveData/PROJ105531/1654258093167634.png)
Question 3
Let X1, X2, X3, X4 be a random sample of size 4 from a standard normal distrubtion. If the statitics W is given by
Then what is the expected value of W?
Question 4
If X ∼ t (19). Then what is the value of the constant C such that P(|X|≤ C) = 0.957
Question 5
Let X1, X2, ….., X10 be independent and identically distributed U(-5, 5) random variables. Then the distribution of the random variables
is
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Apr 12CSIR NET & SET