दो यादृच्छिक चर X और Y को स्वतंत्र कहा जाता है, यदि:

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SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. E (XY) = XE (Y)
  2. E (XY) = E (X) E (Y)
  3. E (XY) = E (X) + E (Y)
  4. E (XY) = YE (X)

Answer (Detailed Solution Below)

Option 2 : E (XY) = E (X) E (Y)
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दो यादृच्छिक चर X और Y स्वतंत्र होते हैं, यदि X और Y के बीच सहप्रसरण शून्य है, जिसे गणितीय रूप से व्यक्त किया जाता है

Cov(X, Y) = E[(X - E[X])(Y - E[Y])] = 0.

यह उनके गुणनफल की उनकी व्यक्तिगत अपेक्षाओं के गुणनफल के बराबर या E (XY) = E (X) E (Y) के बराबर हो सकता है।

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