Difference between revisions of "Homework7 ECE302Fall2008sanghavi" - Rhea

Revision as of 09:00, 15 October 2008

Let $$ F $$ be a non-decreasing function with

$\lim_{x\rightarrow -\infty} F(x) = 0 \mbox{ and } \lim_{x\rightarrow +\infty} F(x) = 1.$

Let $$ U $$ be a uniform random variable on [0,1].

(a) Let $X = F^{-1}(U)$ . What is the CDF of $$ X $$ ? (Note $F^{-1}$ is the inverse of $$ F $$ . A function $$ g $$ is the inverse
(b)How can you generate an exponential random variable from $$ U $$ ?

@@ Line 8: / Line 8: @@
 \mbox{ and } \lim_{x\rightarrow +\infty} F(x) = 1.</math>
-Let $U$ be a uniform random variable on $[0,1]$.
+Let <math>U</math> be a uniform random variable on [0,1].
-\begin{enumerate}
-\item Let $X = F^{-1}(U)$. What is the CDF of $X$?  (Note $F^{-1}$ is the inverse of $F$. A function $g$ is the inverse of $F$ if $F(g(x)) = x$ for all $x$)
+*(a) Let <math>X = F^{-1}(U)</math>. What is the CDF of <math>X</math>?  (Note <math>F^{-1}</math> is the inverse of <math>F</math>. A function <math>g</math> is the inverse
-\item How can you generate an exponential random variable from $U$?
+*(b)How can you generate an exponential random variable from <math>U</math>?
 == Problem 2: Gaussian Generation ==