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I am given a Probability Mass Function for a discrete random variable. From the PMF I computed the Expected Value $E[X]$, the Variance $V[X]$ and the Standard Deviation $S[X]$.

Here is an example (the dotted grey lines are $E[X] - S[X]$ and $E[X] + S[X]$, respectively). We could think about it as a loaded dice with values 0 to 5.

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At this point I have some doubts about how to construct a 99% confidence interval for $E[X]$. Can someone help?

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  • $\begingroup$ Since this is a discrete distribution, you can't really find a 99% confidence interval accurately. Instead, pretend it's a continuous distribution from -0.5 to 5.5 where the chance of getting between 2.5 and 3.5 in the pretend distribution is the chance of getting 3 in the actual distribution. Apply proportionality, so that the chance of getting between 2.7 and 2.8 would be 1/10th that value. Now, simply find numbers a and b whose average is such that the chance of (0,a) is 0.5% and the chance of (b, 5.5) is 0.5%. This will give you a 99% confidence interval, albeit one with decimals in it $\endgroup$
    – Barry Carter
    Commented Jun 16 at 13:40

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