content_image/309430.jpg content_image/309428.jpg content_image/309427.jpg
Lemma 4.5 (i) for each t ∈ R and n ∈ N 

which shows (21) since X$_{N}$$_{(}$$_{n}$$_{)}$ ≤ X$_{N}$$_{(}$$_{n}$$_{+1)}$ . Hence, 

<img src='content_image/309430.jpg'>

<img src='content_image/309428.jpg'>

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Computing the distribution of the second record X$_{N}$$_{(2)}$ is an easy task: Let X$_{1}$ , X$_{2}$ ... be independent copies of the rv X in R d with df F . We make no further assumption on F . Conditioning on X$_{1}$ = y we obtain 

<img src='content_image/309427.jpg'>

