How to find equations for confidence limits in Poisson distribution?

[Mixer]

Homework Statement

What kind of equations you'll get when trying to find confidence limits 100(1-a) % for λ in Poisson distribution?

Homework Equations

Poisson distribution P(X=x) = e^-λ λ^x / x! (x=0,1,2 ...)

The Attempt at a Solution

I made an equation as follows:

Ʃ (k = from k₀ to n) e^-λ λ^k / k! = a/2

to solve the confidence limits. Am I doing correct thing here? I cannot solve λ from that equation + I'm not supposed to have infinite sums in my equations... Any help for me?

 

[mighty2000]

Your equation is not quite correct. To find the confidence limits for λ in a Poisson distribution, we can use the following equation:

P(X ≤ k) = ∑ (k = 0 to n) e-λ λk / k!

where k is the observed number of events, n is the maximum possible value for k, and λ is the mean rate of events.

To find the confidence limits, we can solve for λ by setting P(X ≤ k) = 100(1-a)%, where a is the desired level of confidence. This will give us two values for λ, one for the lower confidence limit and one for the upper confidence limit.

For example, if we want to find the 95% confidence limits for λ in a Poisson distribution, we would set P(X ≤ k) = 95% and solve for λ. This would give us two values, one for the lower limit and one for the upper limit, which we can then use to determine the range of values for λ with 95% confidence.