Question
मान लीजिए X प्राचल और
, वाला एक गामा चर है जिसके
और
हैं।
और
ज्ञात कीजिए। गामा चर का आघूर्ण जनक फलन भी ज्ञात कीजिए और इस प्रकार सिद्ध कीजिए कि आघूर्ण जनक फलन से X का माध्य 6 और X का प्रसरण 3 है।
Answer :
Word Count : 340
गामा वितरण के लिए यदि (X \sim \text{Gamma}(\alpha, \lambda)) हो, तो इसका माध्य और विचलन निम्न सूत्रों से दिया जाता है: [ E(X) = \frac{\alpha}{\lambda}, \quad \text{Var}(X) = \frac{\alpha}{\lambda^2} ] हमें दिया है: [ E(X) = 6, \quad \text{Var}(X) = 3 ] इससे हम (\alpha) और (\lambda) ज्ञात कर सकते हैं। चरण 1: (\lambda) के लिए __________ _________ ____ ____ ______ ____ __________ ____.
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गामा वितरण के लिए यदि (X \sim \text{Gamma}(\alpha, \lambda)) हो, तो इसका माध्य और विचलन निम्न सूत्रों से दिया जाता है: [ E(X) = \frac{\alpha}{\lambda}, \quad \text{Var}(X) = \frac{\alpha}{\lambda^2} ] हमें दिया है: [ E(X) = 6, \quad \text{Var}(X) = 3 ] इससे हम (\alpha) और (\lambda) ज्ञात कर सकते हैं। चरण 1: (\lambda) के लिए __________ _________ ____ ____ ______ ____ __________ ____.
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