PROBABILITY QUESTION Let X have the uniform distribution on

PROBABILITY QUESTION Let X have the uniform distribution on (-pi/2,pi.2), and let Y=tan(X). Find the CDF and a density for Y. What is the name of the distribution of Y?

Solution

CDF of Y = integral ( from -pi/2 , pi/2) tanx dx

= (from -pi/2 ,pi/2) -ln|cosx|

= 0 Answer

PDF = d( -ln|cosx|)/dx

= tanx Answer

Normal Distribution