Could you kindly explain in very simple words, or through examples, what these two sequences mean?
$A_n :=\{X_n > X_i, \;for\; i∈\{0,...,n−1\}\},\\ B_n := \{A_n ∩ A_{n+1}\}.$
I just know that $(X_n)_{n∈N}$ is a sequence of i.i.d. random variables with a continuous distribution function and that $n>1$
Thank you very much in advance!