\fHow can they go from unit normal random variable to the normal distribution by only using X = +Z . For the normal distribution I thought one would have to use: 2 1 E ( e ) = e e 2 tX tx 2 e 2 (x ) +2 tx 2 2 2 (x ) 2 2 2 2 x 2 x + +2 tx 2 2 =e 2 1 dx= e 2 2 2 =e e 2 (x) +2 tx 2 2 2 x 2 x +2 tx 2 2 2 1 e I can't get this calculation done but why is e 2 tx Can you derive that relation in red? dx (x ) 2 2 dx=E ( et ( +Z ) )