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.
$\displaystyle \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.
$\displaystyle
\int\limits_{ - \infty }^\infty {\frac{\lambda }
{{1 + \left( {x - a} \right)^2 }}dx = 1}
$
Probability density function - Wikipedia, the free encyclopedia