let xuniformpi2pi2 and YtanX Find the distribution of Y let

let x~uniform(-pi/2,pi/2) and Y=tanX. Find the distribution of Y.

let x~uniform(-pi/2,pi/2) and Y=tanX. Find the distribution of Y.

P(Y y) = P(tan X y)

P(X arctan y) = 1/ *(arctan y + /2 ) =

1/2 + 1/ arctan y,

thus the density of Y is given by fY (y) = 1 /[*(1 + y^2 )] .

let x~uniform(-pi/2,pi/2) and Y=tanX. Find the distribution of Y. let x~uniform(-pi/2,pi/2) and Y=tanX. Find the distribution of Y.SolutionP(Y y) = P(tan X y) P

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