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-   -   Exercise 1.10 (http://book.caltech.edu/bookforum/showthread.php?t=4621)

LambdaX 09-22-2015 02:46 AM

Exercise 1.10
 
I'm confused as to what part c of Exercise 1.10 is asking. What does it mean by the following?

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"plot estimates for P[|ν-μ| > ε] as a function of ε, together with the Hoeffding bound 2e<sup>-2ε<sup>2</sup>N</sup> (on the same graph)."
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Does this mean to plot P[|ν-μ| > ε] and 2e<sup>-2ε<sup>2</sup>N</sup> each as a separate graph? I can plot  2e<sup>-2ε<sup>2</sup>N</sup> as a function of ε easily, but how would I go about plotting P[|ν-μ| > ε]? Would I define a function that plots the likelihood that |ν-μ| > ε based on the input ε, using the data obtained in part b? Am I on the right track with this thinking?
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Also, is the book asking to plot a separate graph for each graph in b (i.e. ν<sub>1</sub>, ν<sub>rand</sub>, and ν<sub>min</sub>), based on the distribution of ν for each?

LambdaX 09-22-2015 02:56 AM

Re: Exercise 1.10
 
I apologize for the previous format. I can't seem to find a way to edit or delete the thread. Here's a more readable version.

What does it mean by the following?

"plot estimates for P[|ν-μ| > ε] as a function of ε, together with the Hoeffding bound 2e^(-2(ε^2)N) (on the same graph)."

Does this mean to plot P[|ν-μ| > ε] and 2e^(-2(ε^2)N) each as a separate graph? I can plot 2e^(-2(ε^2)N) as a function of ε easily, but how would I go about plotting P[|ν-μ| > ε]? Would I define a function that plots the likelihood that |ν-μ| > ε based on the input ε, using the data obtained in part b? Am I on the right track with this thinking?

Also, is the book asking to plot a separate graph for each graph in b (i.e. ν_1 ν_rand, and ν_min), based on the distribution of ν for each?

magdon 09-24-2015 01:35 PM

Re: Exercise 1.10
 
The problem asks you to compute P[|ν-μ| > ε] from your data for ε equal to (say) 0,0.01,0.02,0.03,....0.5
Now plot this computed probability for each value of epsilon versus epsilon.

Quote:

Originally Posted by LambdaX (Post 12058)
I apologize for the previous format. I can't seem to find a way to edit or delete the thread. Here's a more readable version.

What does it mean by the following?

"plot estimates for P[|ν-μ| > ε] as a function of ε, together with the Hoeffding bound 2e^(-2(ε^2)N) (on the same graph)."

Does this mean to plot P[|ν-μ| > ε] and 2e^(-2(ε^2)N) each as a separate graph? I can plot 2e^(-2(ε^2)N) as a function of ε easily, but how would I go about plotting P[|ν-μ| > ε]? Would I define a function that plots the likelihood that |ν-μ| > ε based on the input ε, using the data obtained in part b? Am I on the right track with this thinking?

Also, is the book asking to plot a separate graph for each graph in b (i.e. ν_1 ν_rand, and ν_min), based on the distribution of ν for each?



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