- #1

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__a__= {a

_{1}, a

_{2}, .., a

_{1000}}, where this set forms a distribution of photoelectrons (pe) seen by a particular photomultiplier tube (pmt) over 1000 repeated events. I then have N sets of these (N pmts), each containing 1000 pe values which I believe are indeed random and independent. So

__a__,

__b__,

__c__, ... (not enough letters!) where a corresponds to pmt

_{1},

__b__corresponds to pmt

_{2}etc.

__a__then goes into a histogram from which a mean and variance is extracted, this is then done for all N sets. I then define N variables pi = μ

_{i}/μ

_{T}where μ

_{i}= mean from histogram i which in turn corresponds to

__a__, and μ

_{T}is the sum of the means (μ

_{i}) from all N histograms.

I'm just now confused on how I'd calculate V[p

_{i}], i.e. for pmt

_{1}given that I know E[

__a__] and V[

__a__]. So far I've thought that perhaps I can say μ

_{T}= μ

_{1}+ μ

_{2}+ ... + μ

_{N}= ((a

_{1}+ a

_{2}+ ... a

_{1000}) + (b

_{1}+ b

_{2}+ ... b

_{1000}) +... )/1000 and then therefore V[μ

_{T}] = ((V[a

_{1}] + V[a

_{2}] + ... V[a

_{1000}]) + (V[b

_{1}] + V[b

_{2}] + ... V[b

_{1000}]) +... )/1000. I'm not sure however, that this is correct.. First of all I don't know if the logic is correct, and secondly I'm not sure whether the a

_{j}, b

_{k}and so on can be treated as independent and random variables (I think they are random and independent, but the means E[

__a__], E[

__b__] etc are not?)

Hopefully this hasn't been too confusing, and any ideas would be greatly appreciated. Cheers.