Question
Download Solution PDFमान लीजिए कि X का pdf\(\rm f(x)=\left\{\begin{matrix}1-|1-x|, 0<x<2& P\left(\frac{1}{3}\le X\le \frac{4}{3}\right)\\\ 0,& \rm otherwise\end{matrix}\right.\), _____ के बराबर है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिए गए प्रायिकता घनत्व फलन (pdf) का उपयोग करके प्रायिकता \(P ({1 \over 3} \leq x \leq {4 \over 3})\) खोजने के लिए, हमें निर्दिष्ट सीमा पर pdf को एकीकृत करने की आवश्यकता है।
pdf \(f(x) = 1 - |1 - x|\) एक खंडशः फलन है। आइए एकीकरण को दो भागों में विभाजित करें:
\(0 < x < 1\) के लिए :
\(f(x) = 1 - (1 - x) = x\)
\(1 \leq x < 2\) के लिए:
\(f(x) = 1 - |1 - x| = 1 - (x - 1) = (2 - x)\)
अब, हम प्रायिकता का मूल्यांकन कर सकते हैं:\(P ({1 \over 3} \leq x \leq {4 \over 3}) = \int\limits_{1\over 3}^{4\over3} f(x) dx \)
समाकल का मूल्यांकन: \([{x^2\over2}]_{1\over3}^{1} + [2x - {x^2\over 2}]_{1}^{4\over3}\)
इसे सरल बनाते हुए, हमारे पास है:\(({1\over 2} - {1\over 18}) + ({8 \over 3} - {8\over 9} - 2 + 1) = {13\over 18}\)
अतः, अभीष्ट प्रायिकता \(13\over 18\) है।
Last updated on Jul 2, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> TNPSC Group 4 Hall Ticket 2025 has been released on the official website @tnpscexams.in
-> HSSC Group D Result 2025 has been released on 2nd July 2025.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> Candidates should also use the SSC CGL previous year papers for a good revision.
->The UGC NET Exam Analysis 2025 for June 25 is out for Shift 1.