Joonsoocomment - Rhea

A slecture by Joonsoo Kim

Please leave me comment below if you have any questions, if you notice any errors or if you would like to discuss a topic further.

Review by Khalid Tahboub:

Great job! few minor remarks:

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

4) I think it might give a nice demonstration if you plot the histogram of U and X to show that this method really functions in the desired way.

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