Line 26: Line 26:
 
: Find c by,
 
: Find c by,
 
: <math>\int_{-\infty}^{\infty} f_{X}(x)dx =1.</math>
 
: <math>\int_{-\infty}^{\infty} f_{X}(x)dx =1.</math>
: <math>f_{X|A}(x|A)= \frac{f_{X}(x)}{P({X>3})} = \frac{f_{X}(x)}{1- F_{X}(3)} .</math> -TA
+
: <math>f_{X|A}(x|A)= \frac{f_{X}(x)}{P({X>3})} = \frac{f_{X}(x)}{1- F_{X}(3)}</math> for some range of x
 +
-TA
  
 
===Comment on Hint===
 
===Comment on Hint===

Latest revision as of 09:17, 27 March 2013

Practice Problem: What is the conditional density function


Let X be a continuous random variable with probability density function

$ f_X(x)=\left\{ \begin{array}{ll} c x^2, & 1<x<5,\\ 0, & \text{ else}. \end{array} \right. $

Let A be the event $ \{ X>3 \} $. Find the conditional probability density function $ f_{X|A}(x|A). $


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You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!


Hint

Hint:

Find c by,
$ \int_{-\infty}^{\infty} f_{X}(x)dx =1. $
$ f_{X|A}(x|A)= \frac{f_{X}(x)}{P({X>3})} = \frac{f_{X}(x)}{1- F_{X}(3)} $ for some range of x

-TA

Comment on Hint

It's important to note that the $ \color{blue} f_X(x) $ given in the final line of the hint is distinct from the pdf given in the problem statement. Specifically, the new $ \color{blue} f_X(x) $ is nonzero only on the range dictated by the occurrence of event 'A' such that
$ \color{blue} f_X(x)=\left\{ \begin{array}{ll} c x^2, & 3<x<5,\\ 0, & \text{ else}. \end{array} \right. $
Note that this is 'new' $ \color{blue} f_X(x) $ is not a valid pdf by itself (violates normalization to 1 axiom), and thus the normalizing denominator is used. -ag
    • Correct. -pm

Answer 1

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Answer 2

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Back to ECE302 Spring 2013 Prof. Boutin

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BSEE 2004, current Ph.D. student researching signal and image processing.

Landis Huffman