- #1
Naumberg
- 1
- 0
Problem:
"Let [itex]x_1, ..., x_n[/itex] be i.i.d random variables uniformly on [0,1]. Let [itex]X[/itex] be the length of the longest increasing subsequence of [itex]x_1, ..., x_n[/itex]. Show that [itex]E[X] \ge (1-o(1))(1-e^{-1}) \sqrt{n}[/itex]."
Hi forum!
Using the Erdos' lemma I can only deduce that [itex]E[X] \ge \frac{1}{2} \sqrt{n}[/itex], which is a weaker bound unfortunately.
I would appreciate any further ideas!
Thanks for your help,
Michael
"Let [itex]x_1, ..., x_n[/itex] be i.i.d random variables uniformly on [0,1]. Let [itex]X[/itex] be the length of the longest increasing subsequence of [itex]x_1, ..., x_n[/itex]. Show that [itex]E[X] \ge (1-o(1))(1-e^{-1}) \sqrt{n}[/itex]."
Hi forum!
Using the Erdos' lemma I can only deduce that [itex]E[X] \ge \frac{1}{2} \sqrt{n}[/itex], which is a weaker bound unfortunately.
I would appreciate any further ideas!
Thanks for your help,
Michael