I have 60 numbers drawn from a normal distribution with mean 0 and standard deviation of 1.
I then take the sum of the 60 values.
I do this 1000 times and plot a histogram of the various sums I get:
And I am able to fit the histogram with a normal distribution with a mean of 0 and a standard deviation of sqrt(60).
So far so good.
I now want to square each of my 60 numbers to get (for example) a realization like this:
If I again take the sum of the 60 values and repeat 1000 times I get a different histogram:
My question: what function do I use to fit this histogram? Is it another normal distribution? Maybe chi-squared? What parameters do I use?