Category:Tangent of Uniform Distribution has Standard Cauchy Distribution

This category contains pages concerning Tangent of Uniform Distribution has Standard Cauchy Distribution:

Let $X$ be a continuous random variable with a uniform distribution on the closed real interval $\closedint {-\dfrac \pi 2} {\dfrac \pi 2}$:

$X \sim \ContinuousUniform {-\dfrac \pi 2} {\dfrac \pi 2}$

Let $Y$ be a continuous random variable such that:

$Y = \tan X$

where $\tan$ denotes the tangent function.

Then $Y$ has the standard Cauchy distribution:

$Y \sim \Cauchy 0 1$