Distribution of Scaled Minimum from Shifted Exponential Sample| UPSC ISS 2025 Paper-1 | Problem-57
Автор: RitwikMath
Загружено: 2025-10-11
Просмотров: 33
Описание:
This video explains the distribution of \( 2n(M - \theta) \), where \(M\) is the minimum of a random sample of size \(n\) from a shifted exponential distribution with pdf \(f(x) = e^{-(x-\theta)}\) for \(x \geq \theta\). It shows that \(M - \theta\) follows an exponential distribution with rate \(n\), and thus \(2n(M - \theta)\) follows a chi-square distribution with 2 degrees of freedom. A clear demonstration of minimum order statistics and related distributions.
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#exponentialdistributionproblemsandsolutions #chisquare #orderstatistics
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