Difference between revisions of "Joonsoocomment" - Rhea

Revision as of 19:36, 1 May 2014

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

@@ Line 11: / Line 11: @@
 <center><math>
 F^{-1}(u)=inf\{ x|F(x)\leq u, \quad u\in [0, 1] \}
+</math></center>
+) How we reach <center><math>
+X <- F^{-1}(U)\quad
+</math></center> from <center><math>
+F^{-1}(u)=inf\{ x|F(x)\geq u, \quad u\in [0, 1] \}
+</math></center> is not very clear to me
+)I think the equation
+<center><math>
+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
+</math></center>
+should be instead
+<center><math>
+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>