# Interesting statistics problem

1. Apr 9, 2013

### Pascal22

Suppose that there are m independent and identically distributed variables Y1, Y2, ... Ym. Yi - are random variables. Let Y denote the maxof Y1, Y2, ... Ym. What's the distribution of Y when m is very big?

Thank you for any help, in advance.

2. Apr 9, 2013

### mathman

P(Y<y) = P(Y1<y)P(Y2<y).....P(Ym<y) = P(Y1<y)m (independent and identially distributed).

3. Apr 9, 2013

### Pascal22

Thanks a lot!

Do I understand correctly? That CDF of Y will converge 0?

Last edited: Apr 10, 2013
4. Apr 10, 2013

### mathman

It depends. If the Yk are distributed so that P(Yk < y) < 1, yes. However if the Yk are bounded, then no.

5. May 28, 2013