Cauchy distribution

• October 27th 2008, 11:55 AM
totalnewbie
Cauchy distribution
I was said to find lambda:
I have no idea about that. What is that and how to find? I know that it's 1/pi but don't know how and why.
• October 27th 2008, 12:23 PM
Peritus
$\lambda$ is the normalization coefficient of the probability density function it's there to make sure that the p.d.f. is legal: The total integral of the p.d.f. must equal 1, which means that the sum of the probabilities that the r.v. is in some interval equals 1.

$
\int\limits_{ - \infty }^\infty {\frac{\lambda }
{{1 + \left( {x - a} \right)^2 }}dx = 1}
$

Probability density function - Wikipedia, the free encyclopedia