minimum of chi-squared distribution

#1
Hi

I have a query on finding the minimum of a chi-squared distribution (M).

I have attached my working so far. But I have difficulty evaluating the density function of M. How could this be reduced to a simplified form

Any help would be much appreciated.

Thank you
 

Dason

Ambassador to the humans
#9
Well one suggestion would be that you don't need to try to evaluate the pdf at all. Just consider the CDF. What would the cdf look like in terms of the cdf of the original distribution?
 

Dason

Ambassador to the humans
#10
You don't need the pdf. Start from the definition of Cdf. You can figure out the cdf of the min with respect to the cdf of the original random variable with no need to calculate the pdf.