Interesting statistics problem

Forum for the GRE subject test in mathematics.
Pascal22
Posts: 3
Joined: Tue Apr 09, 2013 11:05 am

Interesting statistics problem

Postby Pascal22 » Tue Apr 09, 2013 12:01 pm

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.

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redcar777
Posts: 34
Joined: Sun Nov 04, 2012 11:59 am

Re: Interesting statistics problem

Postby redcar777 » Tue Apr 09, 2013 12:09 pm

The CDF of Y = max( Y1, Y2, .. Yn) is the product of the CDF of each Yi... does that help?

Pascal22
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Joined: Tue Apr 09, 2013 11:05 am

Re: Interesting statistics problem

Postby Pascal22 » Wed Apr 10, 2013 7:04 am

Thanks a lot!

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

dollar
Posts: 16
Joined: Wed Feb 27, 2013 8:01 pm

Re: Interesting statistics problem

Postby dollar » Wed Apr 10, 2013 7:24 am

No, for example if Y_i are all Bernoulli, then the CDF of the max will clearly not converge to 0.

However, if Y_i has unbounded positive support, then yes, the cdf will converge pointwise to 0.

Pascal22
Posts: 3
Joined: Tue Apr 09, 2013 11:05 am

Re: Interesting statistics problem

Postby Pascal22 » Wed Apr 10, 2013 8:13 am

Ok, let's try express CFD of Y in terms of given variables:
1. The probability of the event Yi is 1/n.
2. The CFD of Y is F(Y) = F(Y1)^n.

Therefore, F(Y) = (1/n)^n. Am I right? I need to express CFD of Y through the given parameters.




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