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Let X1, …, X7 and Y1, …, Y9 be two random samples drawn independently from two populations with continuous CDFs F and G respectively. Consider the Wald-Wolfowitz run test in the context of the following two sample testing problems: H0: F(x) = G(x) ∀ x vs. H1: F(x) ≠ G(x) for some x. If the random variable R denotes the total number of runs in the combined ordered arrangement of the two given samples, then which of the following is true?

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CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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  1. PH0(R = 6) = \(\frac{28}{286}\), PH0(R = 9) = \(\frac{28}{143}\)
  2. PH0(R = 6) = \(\frac{21}{286}\), PH0(R = 9) = \(\frac{15}{280}\)
  3. PH0(R = 6) = \(\frac{21}{286}\), PH0(R = 9) = \(\frac{28}{143}\)
  4. PH0(R = 6) = \(\frac{21}{286}\), PH0(R = 9) = \(\frac{15}{286}\)

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Option 3 : PH0(R = 6) = \(\frac{21}{286}\), PH0(R = 9) = \(\frac{28}{143}\)
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The Correct Answer is option 3 

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