Definition:Cauchy Distribution/Also defined as

Cauchy Distribution: Also defined as
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \R$. The Cauchy Distribution of $X$ can be found defined in the simplified form:


 * $\map {f_X} x = \dfrac 1 {\pi \paren {1 + x^2} }$

which is obtained from the full form by setting:
 * $\lambda = 1$
 * $\gamma = 0$

Some sources give it as:
 * $\map {f_X} x = \dfrac 1 {\pi \paren {1 + \paren {x - \gamma}^2} }$

which is obtained from the full form by setting $\lambda = 1$.