Relation between Rayleigh and exponential distribution in the following?

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I am reading a paper. In the following image, as I understand, the transition lengths should be exponentially distributed. However, the author's claim it to be Rayleigh distributed. Also, what does eq. 1 suggest (My idea is that the Transition-lengths $l$ are exponentially distributed with intensity $\lambda$, but then why do we have $\pi l^2$)

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