DES - Demonstration on the Memory-Less Property of the Exponential Distribution

Arguments:

• DES - Exponential Distribution
• DES - Definition of ‘Memory-Less Property’

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Demonstration that the exponential distribution enjoys the memory-less property:

From the definition of conditional probability we have:

$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

Where $P(A\cap B)$ is usually wrote as: $P(A,B)$

We can that $P(X>t+s|X>t)=P(X>t+s)$ because logically if $X>t+s$ is obvious that it will be $X>t$, (as $s$ is $\ge 0$).