I have the random indicator variable $X$, which takes $1$ if the person has covid and $0$ otherwise. I have calculated $Prob(X_i = 1)$ (so the ${E[X_i]}$or expectation of $X_i$) over the course of $137$ days.
The next question is to "Derive confidence intervals for your estimates of $Prob(X_0 = 1)$ using the CLT and Chebyshev Inequality and plot these confidence intervals vs time, e.g. as error bars about the estimates of $Prob(X_0 = 1)$."
So I got my array of $E[X_i]$ 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???
