Confirm Normalization: Is Something Wrong?

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Somefantastik
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Hey folks.

I was asked to confirm that the attached discrete function is normalized.

The function to check the normalization that I was provided with is

\frac{1}{2}\sum^{N}_{i = 1}P_{i}(\Theta)\Delta\Theta_{i} = 1

No matter what I do, I get a number on the order of 10^4, not anything close to 1.

Is there something wrong with the data, or is there something wrong with me? If you look at the first couple of values, you can see that the value is >>1 which I don't understand how I can ever bring that down.
 

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My guess is that the question might be to find the normalization. You are right in that it is not normalized.
 
Perhaps. That means my formula is wrong. What is the process usually used to normalize a discrete function like this?
 

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