If X1, X2, … Xn is a simple random sample without replacement of size n from a finite population of N units with mean μ and variance σ2, the covariance of (Xi,Xj) will be:

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SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. \(\dfrac{-\sigma^2}{N-1}\)
  2. \(\dfrac{\sigma^2}{N-1}\)
  3. \(\dfrac{\sigma^2}{n-1}\)
  4. \(\dfrac{-\sigma^2}{n-1}\)

Answer (Detailed Solution Below)

Option 3 : \(\dfrac{\sigma^2}{n-1}\)
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Detailed Solution

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Explanation 

If x1, x2--------------,xn is a single random sample without replacement of size n is from a finite population N with mean μ and variance σ2 the covariance(xi, xj) is given by

∴ Cov(xi, xj) = σ2/(n – 1)

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