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Exercise 1 . Separating two GaussiansExercise 2 . Define a zero - mean Gaussian function as ( x ; 0 , 2 ) = 1
Exercise Separating two GaussiansExercise
Define a zeromean Gaussian function as
;exp
We want to approximate the Gaussian function using a boxcar function
;
Find the best that can achieve this. Hint: Go to Wikipedia and learn the concept of KLdivergence.
Suppose you have two Gaussians located at and respectively, ie Gaussian; and Gaussian;
We know that if is large enough, then the two Gaussians will be separated. We also know that if is
small enough, the two Gaussians will be separated. Fix What is the largest you can have before the
two Gaussian become merged together? By merge, I mean that you will no longer be able to see the two
peaks. The figure below is an example for As you can see, when the two Gaussians cannot
be distinguished. Use paper and pencil to answer this question, and use PythonMATLAB to verify your
answer.
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