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What is the mean and std dev of the minimum of 6 random variables having a normal distribution?

Asked by on January 16, 2014

Let’s say the average height of people is 150cm, with a std dev of 20cm, and their heights are normally distributed. Now if I group these people randomly in groups of 6 people, and I just take the height of the shortest person in each group. What is the mean and std dev of these shortest people?




The One Who Knows (Swamy)

August 13, 2007 at 1:33 am

Without doing any maths, I would guess that the mean would be 147 cm and the standard deviation would remain same. But I could be wrong since I left statistics long ago.



August 13, 2007 at 1:44 am

This is “Order Statistics”

It is straigthforward to write the expression of the mean and variance but the computation is to be given to a math engine (MATLAB is my prefered)


Wala Lang  

August 13, 2007 at 4:46 am

The cumulative distn of the minimum is 1-[1-F(x)]^6 and its pdf is 6{[1-F(x)]^5}f(x), where F(x) is the normal cdf and f(x) is normal pdf.
You can use either the cdf or pdf to derive the mean and variance.

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