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Math Help - Cauchy distribution

  1. #1
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    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.
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  2. #2
    Senior Member Peritus's Avatar
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    \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.

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

    Probability density function - Wikipedia, the free encyclopedia
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