## Suppose we want

*p*(*y*)*dy*=*e*-*y**dy*,*y***[0*,∞*)*.*## Apply the transformation method:

- Have
*f*(*y*) =*e*-*y*,*F*(*y*) =*e*-0 -*e*-y = 1 -*e*-y. - Set
*x*=*F*(*y*)/*F*(*∞*) and solve*x*(1 -*e*-*∞*) = 1 -*e*-*y*for*y*. - Get
*y*(*x*) = -ln(1 -*x*).

- Have
## So if

*x*is a uniform deviate between 0 and 1,*y*(*x*) (*x*< 1) will be an exponential deviate.## See

*NRiC*§7.2 for Gaussian deviates.