Question
Download Solution PDFयदि 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
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसूत्र
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।
Last updated on Jul 8, 2025
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