Question

Let X be Uniformly distributed over the interval [0,π/2][0,π/2]. Find the density function for Y=sinXY=sin⁡X. Evaluate the density function (to 2 d.p.) at the value 0.1.

the density function is ?

Answer 1

solution The density for fonction of x is barco) , (05xçule) TT Given, y = Sin xy = sinx The CDF of Y is tu (Y) = plysy) - p (sinx + y ) - P ( x <sinly ) Sig fy() s dx - siol (y) B; () - test sca" () The density function of yes - fy(Y) = 2 2 F (4) when aao y=sino =0 Tvz when a = T)e , Y = Si Ther, fax) = p my hand pot i = 0.1 for Cov) = CODE = 0.64 I when neattle, y = sin (I) = 1)