Category:Quotient of Gaussian Distributions has Cauchy Distribution
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This category contains pages concerning Quotient of Gaussian Distributions has Cauchy Distribution:
Let $X$ and $Y$ be independent continuous random variables each with a Gaussian distribution with zero expectation:
| \(\ds X\) | \(\sim\) | \(\ds \Gaussian 0 { {\sigma_x}^2}\) | ||||||||||||
| \(\ds Y\) | \(\sim\) | \(\ds \Gaussian 0 { {\sigma_y}^2}\) |
Let $U$ be the continuous random variable defined as:
- $U = \dfrac X Y$
Then $U$ has the Cauchy distribution:
- $U \sim \Cauchy 0 \lambda$
where:
- $\lambda = \dfrac {\sigma_x} {\sigma_y}$
Pages in category "Quotient of Gaussian Distributions has Cauchy Distribution"
The following 2 pages are in this category, out of 2 total.