I Standard deviation and count rate

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The discussion centers around the relationship between standard deviation and count rate in the context of radiation counting experiments. Participants clarify that counting rates follow a Poisson distribution, which approximates a Gaussian distribution at reasonable rates, leading to a 95% probability within ±2σ. However, there is confusion regarding the assertion that 2σ equals 0.05 times the count rate. The standard deviation for count rate is actually derived from the formula (r/t)^(1/2), where r is the count rate and t is the counting time. Ultimately, the consensus is to disregard the incorrect statement about the relationship between 2σ and count rate.
Zuzana
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Hello,

I watched MIT course on Nuclear physics (13. Practical Radiation Counting Experiments on ytb) and I do not understand why 2*sigma (standard deviation) = 0.05* countRate. As far as I know, integral of normal distribution from -2sigma to 2 sigma gives 95 % probability, but how can 2*sigma equals 100%-95% of count rate?

Thank you for the answer.
 
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Hello @Zuzana,
:welcome: ##\qquad##!
As you may know, a counting rate obeys a Poisson distribution. ( e.g. sheet 17 here ). For reasonable counting rates, such a Poisson distribution is very close to a Gaussian distribution ( ibid sheet 20 ). Hence the 95%.

##\ ##
 
u = measured mean
s = measured standard deviation

There is a 95% chance that the true mean lies in the interval
-1.96s+u to u+1.96s
 
Hornbein said:
u = measured mean
s = measured standard deviation

There is a 95% chance that the true mean lies in the interval
-1.96s+u to u+1.96s
yes, I understand this, but I do not understand why should 2*sigma = 0.05*countRate.
 
I don't know where you got that the standard deviation of count rate is count rate but the standard deviation for count rate r is r1/2 / t1/2 or (r / t)1/2 where t is the counting time.

Zuzana said:
and I do not understand why 2*sigma (standard deviation) = 0.05* countRate.
I don't understand this statement either. Perhaps you misinterpreted something in the video.

95% are between ±2σ meaning 5% is outside this interval or 2.5% above and 2.5% below.
 
Zuzana said:
yes, I understand this, but I do not understand why should 2*sigma = 0.05*countRate.
I don't understand it either. I'd say you should disregard this confused concept.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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