In summary, I have the random indicator variable X, which takes 1 if the person has covid and 0 otherwise. I have calculated Prob(Xi = 1) (so the E[Xi] / expectation of X) over the course of 137 days.

The next question is to "Derive confidence intervals for your estimates of Prob(X0 = 1) using the CLT and Chebyshev Inequality and plot these confidence intervals vs time, e.g. as error bars about the estimates of Prob(X0 = 1)."

So I got my array of E[Xi] values, and for each day I calculated the mean and standard deviation based on that day and all previous days and then did my calculations.

This leads to 95% confidence intervals that seem to grow and grow (graph) Is this correct? what does this imply? Is it not incorrect to create confidence intervals on this time based sampling anyways???