Difference between revisions of "Joonsoocomment" - Rhea

Revision as of 19:45, 1 May 2014

This slecture was 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

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.

@@ Line 1: / Line 1: @@
-This slecture will be reviewed by Khalid Tahboub:
+This slecture was reviewed by Khalid Tahboub:
 ) I think the first equation should be
 <center><math>
 F^{-1}(u)=inf\{ x|F(x)\geq u, \quad u\in [0, 1] \}
@@ Line 28: / Line 26: @@
 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
 </math></center>
+) 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.