(New page: X is exponential RV with unknown parameter lambda, which we want to find. Sample X=x <math>f_X(x;\lambda)=\lambda e^{-\lambda x}</math> Therefore: <math>\lambda^{hat}_{ML}=max(\lambda...)
 
 
Line 1: Line 1:
 +
[[Category:ECE302Fall2008_ProfSanghavi]]
 +
[[Category:probabilities]]
 +
[[Category:ECE302]]
 +
[[Category:problem solving]]
 +
 
X is exponential RV with unknown parameter lambda, which we want to find.
 
X is exponential RV with unknown parameter lambda, which we want to find.
  
Line 17: Line 22:
  
 
<math>\lambda^{hat}_{ML}=\frac{1}{x}</math>
 
<math>\lambda^{hat}_{ML}=\frac{1}{x}</math>
 +
----
 +
[[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]]

Latest revision as of 13:36, 22 November 2011


X is exponential RV with unknown parameter lambda, which we want to find.

Sample X=x

$ f_X(x;\lambda)=\lambda e^{-\lambda x} $

Therefore:


$ \lambda^{hat}_{ML}=max(\lambda e^{-\lambda x}) $

$ \frac{\delta}{\delta\lambda}(\lambda e^{-\lambda x})=e^{-\lambda x}-\lambda e^{-\lambda x}=0 $


Solving for lambda gives us:


$ \lambda^{hat}_{ML}=\frac{1}{x} $


Back to ECE302 Fall 2008 Prof. Sanghavi

Alumni Liaison

EISL lab graduate

Mu Qiao