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.

## Interesting statistics problem

### Re: Interesting statistics problem

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

### Re: Interesting statistics problem

Thanks a lot!

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

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

### Re: Interesting statistics problem

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.

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

### Re: Interesting statistics problem

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.

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.