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N˘F or X 1;;X n˘p 4 Transformations Let Y = g(X) where g R !R Then F Y(y) = P(Y y) = P(g(X) y) = Z A(y) p X(x)dx where A(y) = fx g(x) yg The density is p Y(y) = F0 Y (y) If gis strictly monotonic, then p Y(y) = p X(h(y)) dh(y) dy where h= g 1 Example 3 Let p X(x) = e x for x>0 Hence F X(x) = 1 e x Let Y = g(X) = logX Then F Y(yZ z z f h q wu d od y h q x h f k u \ v oh u mh h s f r p h h s wk h x q g lv s x wh g lq j r i wk h r ii u r d g d g y h q wx u h lq y lwh v \ r x wr f olp e lq wr wk h g u ly h uA p V Ali Pasa g R *2178html C X p C ` F Ispajce u K A i s j *1362html C ` E } i C Eench Eemanae A j A *97html @ l X R x F Y b g E n V F Organis Liskooriskovy Krem 1000g Organis "¯^ x[V[g p[} "Y