Is showing that the exponential dbn is the only memoryless dbn equivalent to showing that the weibull is NOT memoryless?

This seemed like a lot of work for 2 marks (the proof we did on day 1 I mean).

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So there are two ways to show this for any continuous distribution.

- Showing that the exponential distribution is the only continuous distribution that has the memoryless property is equivalent to showing that any other continuous distribution does not have the memoryless property.
- Let \(X\) be any continuous random variable. In order to show that \(X\) does not have the memoryless property, you need to show that: $$ Pr(X>s+t|X>t) \neq Pr(X>s)$$

That being said, both methods do take a bit of time so I suggest you use the method that is most comfortable for you.

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Thanks

We were leaning towards 1 but seeing as the Q was only 2 marks - we thought this was too much work?

Also - 2 isn't really possible becuase we are only given the intensity funtion of the Weibull dbn and not its actual pdf or is there another way?