LFD Book Forum Exercise 1.10
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#1
09-22-2015, 02:46 AM
 LambdaX Junior Member Join Date: Sep 2015 Posts: 2
Exercise 1.10

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

HTML Code:
`"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)."`
HTML Code:
`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?`
HTML Code:
`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?`
#2
09-22-2015, 02:56 AM
 LambdaX Junior Member Join Date: Sep 2015 Posts: 2
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?
#3
09-24-2015, 01:35 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
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 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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