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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

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 75^th percentile of the statistics

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

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Apr 12CSIR NET & SET