Memoryless Property Proof: Why the Exponential Distribution is Unique ?| Stats + DE Explained
Автор: Towards Infinity
Загружено: 2025-09-23
Просмотров: 283
Описание:
In this video, we dive into one of the most elegant results in probability theory: the exponential distribution is the only continuous distribution that satisfies the memoryless property.
We start by explaining what memoryless-ness means in simple terms.
We also discuss the hazard rate interpretation, why other distributions fail to be memoryless, and give a numerical example to make the conditional probability simplification crystal clear.
By the end, you’ll have a solid understanding of why memorylessness implies exponential — and the intuition behind one of probability’s most important properties.
Perfect for: students of probability, statistics, stochastic processes, or anyone who loves seeing theory meet intuition.
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