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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

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett