But you might wonder why one might want to estimate things like \(\mu, p, \sigma\) or any of the other theoretical statistics. You should note that in each of the distributions noted in this text certain parameters were needed before one could proceed. For example, with the binomial, one must know n and p. For the exponential, one must know \(\mu\text{.}\) Where do you think these parameters come from? Likely from past experience where a history of results leads to an \(\overline{x}\) that would be a reasonable value to presume for \(\mu\text{.}\) Taking the observed value as the theoretical value allows you to subsequently use the formulas provided for each of the distributions. But is this sensible and does the resulting probabilty function correspond to realistic probability calculation?