माना कि X1 तथा X2 माध्य μ तथा धनात्मक निश्चित प्रसरण आव्यूह ∑ वाले दो i.i.d p × 1 बहुचर प्रसामान्य यादृच्छिक सदिश हैं। तब निम्न यादृच्छिक चरों में से किस का हमेशा एक केंद्रीय ची-स्क्वायर वितरण होता है

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. (X1 - X2)T (X1 - X2)​
  2. 2(X1 - X2)T (X1 - X2)
  3. 2(X1 - X2)T-1(X1 - X2)
  4. (X1 - X2)T-1(X1 - X2)

Answer (Detailed Solution Below)

Option 4 : (X1 - X2)T-1(X1 - X2)
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(X1 - X2)2 का केंद्रीय χ² बंटन होता है।

विकल्प (4) सही है।

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