# Why I get wrong pdf if i multiply two Cauchy distributions?

From this website, i see that i can multiply two pdf to get the pdf of joint distribution. http://www.math.uah.edu/stat/dist/Joint.html

However, I cannot get the answer in wiki if I multiply two Cauchy distributions. https://en.wikipedia.org/wiki/Cauchy_distribution $$f(x, y; x_0,y_0,\gamma)= { 1 \over 2 \pi } \left[ { \gamma \over ((x - x_0)^2 + (y - y_0)^2 +\gamma^2)^{1.5} } \right]$$

for example,

$$(\frac{1}{\pi}\frac{1}{1+x^2})(\frac{1}{\pi}\frac{1}{1+y^2})\neq{1 \over 2\pi} \left[ { 1 \over (x^2 + y^2 +1)^{1.5} } \right]$$

Why?

• Since the r.h.s. is a joint pdf of two dependent r.v.'s, and the l.h.s. is a joint pdf of two independent r.v.'s. – NCh Jul 2 '17 at 1:53