Confidence Interval  Poisson
Considering X ~ Poi(?). Based on observations x1, ..., x100, iid and with the same distribution as X, we can estimate the confidence interval [0.3;1.8] for ?. Find the confidence interval, with the same coverage probability for P {X<=2}. TIP: express P {X<=2} in terms of ?
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Don't you need to calculate the probability coverage? From what I understood you would need to calculate the probability coverage for the first given interval and then use it to find another interval with P{X<=2} with the same probability coverage. How did you skip not finding it?

What do you mean by probability coverage? You know that with certain confidence level lambda in inside the given interval. So with the same confidence level, P[x <=2] will lie in the interval I computed. There doesn't seem to be a need to compute anything else.

Sorry, some terms might get lost in translation. Coverage probability I mean the percentage of chance of lambda being inside the confidence interval. So I was thinking you would need to calculate the percentage of chance of lambda being inside [0,3;1,8] and use this same percentage to determine the other confidence interval for P[X>=2]

No, that percentage of chance is not given for lambda, and hence you can not find it for p[X<=2]. That percentage of chance is unknown but is the same for both confidence intervals.

But how can you be certain that is the same for both?

It is because the second interval is directly computed from the first interval, so the probability of both intervals are the same.

Makes sense. Why does he mention this coverage probability though? It seems like it wouldn't change your answer with your without it

The problem does not ask for the coverage probability. It just wants it to be the same.
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