pylab inline

from scipy.stats import chi2,norm
import numpy as np

df=1
rv=chi2(df)
x=np.linspace(0,10)
chi2pdf=rv.pdf(x) 
plot(x,chi2pdf),ylim([0,0.5])

v=norm.rvs(size=10000)
v2=v*v
h,bin_edges=np.histogram(v2,bins=100,density=True)
bin_center=(bin_edges[1:]+bin_edges[:-1])/2.
bar(bin_center,h,width=0.2);plot(x,chi2pdf,'r-');xlim([0,10]);ylim([0,0.5]) 

df=2
rv=chi2(df)
x=np.linspace(0,10)
chi2pdf=rv.pdf(x)
plot(x,chi2pdf),ylim([0,0.5])

v1=norm.rvs(size=10000);v2=norm.rvs(size=10000)
v=v1+v2*1j
vabs=np.abs(v)**2
h,bin_edges=np.histogram(vabs,bins=100,density=True)
bin_center=(bin_edges[1:]+bin_edges[:-1])/2.
bar(bin_center,h,width=0.2);plot(x,chi2pdf,'r-');xlim([0,10]);ylim([0,0.5])