I have interviews coming up with Optiver, Virtu, Jane Street, etc.. These companies like to ask candidates for confidence intervals for their answers. While this usually not too difficult to do, I'm curious about what interval to give if I'm certain of my answer. Let's say I'm asked to determine the sum of the integers from 1 to 100, which I know to be 5050, do I say [5050,5050] is my confidence interval or do I give a wider range, so I don't seem "overconfident"?
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If it's that simple of a question and you really are that confident in your answer, feel free to say [5050, 5050] as your answer. I only ever got asked for confidence intervals when the thing wasn't as exact (i.e. what's the current temperature outside, what will it be at midnight tonight, what's the population of Chicago).
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