यदि यादृच्छिक चर X को पैरामीटर n = 5, p = 0.4 के साथ द्विपद रूप से वितरित किया जाता है, तो Y का तीसरा भाज्य आघूर्ण बराबर होता है

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SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )
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  1. 0.384
  2. 3.84
  3. 0.768
  4. 7.68

Answer (Detailed Solution Below)

Option 2 : 3.84
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सूत्र

द्विपद वितरण का प्रायिकता वितरण फलन इस प्रकार है:

F(x) = ncxpxqn – x

भाज्य आघूर्ण = ncrpr!r

X = 0, 1, 2 ---n

p = सफलता की घटना की प्रायिकता

q = 1 – p = घटना के विफल होने की प्रायिकता

गणना

द्विपद वितरण के भाज्य आघूर्ण के सूत्र के अनुसार

⇒ E[(X)r] =  5c3(0.4)3!3

⇒ [5!/(3!(5 – 3)!](0.4 × 0.4 × 0.4)!3

⇒ [5!/3! × 2!](0.064(3)

 E[(X)r] का मान 3.84 है। 

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