Joonsoocomment - Rhea

This slecture will be reviewed by Khalid Tahboub:

1) I think the first equation should be

F^{-1}(u)=inf\{ x|F(x)\geq u, \quad u\in [0, 1] \}

instead of

F^{-1}(u)=inf\{ x|F(x)\leq u, \quad u\in [0, 1] \}

2) How we reach

X <- F^{-1}(U)\quad

from

F^{-1}(u)=inf\{ x|F(x)\geq u, \quad u\in [0, 1] \}

is not very clear to me

3)I think the equation

F(x) = \int_{-\infty}^x \lambda exp(-\lambda x') dx' = \int_0^x \lambda exp(-\lambda x') dx' = [-exp(-\lambda x')]_0^x = 1-exp(-\lambda x) \leq u

should be instead

F(x) = \int_{-\infty}^x \lambda exp(-\lambda x') dx' = \int_0^x \lambda exp(-\lambda x') dx' = [-exp(-\lambda x')]_0^x = 1-exp(-\lambda x) \geq u

Alumni Liaison