Estimation of the number of background events

[Bolte Dela Paz]

Homework Statement

Estimation of the number of background events

Relevant Equations

aa

The problem is;

You are designing an experiment to search for a new particle. Based on some model, the number of expected signal events is estimated to be 10. In order to claim the signal with the confidence level of 3σ (or 5σ), how small the expected number of background events should be?

I don't know how to solve this. Please give me some hints. Thank you.

 

[BvU]

Hello and !

First hint: post your relevant equations. 'aa' doesn't do any good.
If you have no idea at all, consult a relevant textbook.
Then: post your own attempt, as per
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

so our helpers are allowed to help at all ...

 

[haruspex]

See if https://www.physi.uni-heidelberg.de/~nberger/teaching/ws13/statistics/exercise10.pdf helps.

 

[haruspex]

If it helps, my understanding of the problem, given the text at that link, is this...

Suppose you plan to conduct N experiments, and the theory to be tested tells you that you expect $N\lambda_S=10$ 'signal' events.
You also know to expect $N\lambda_B$ 'background' events even if the theory is false. These are events that cannot be readily distinguished from signal events. By chance you might observe more than $N\lambda_B$ events, so be led into thinking you had seen some signal events. The question is, how large can $N\lambda_B$ be and yet you are $3\sigma$ confident that at least some are signal events?
(I think you may have to assume that at least $N(\lambda_B+\lambda_S)$ events are observed.)