I agree with swuehl. One row per patient per day in the hospital, built using the linked approach.
I gather that MRN is the patient ID? Once you have the table built, the expression should be this simple.
count(distinct MRN)
The remaining question is how you want to select a time frame. I usually just use Date, Month, and Year fields. Things get more complicated if you want to make it easy for the user to select an arbitrary from and to date, and count all patients that were in the hospital at some point in that range. This is perhaps most typically done with two variables in two calendar objects, and either triggering the selection of dates in range of those variables, or using set analysis in the count expression. I just posted another option over here. I'm sure we can help you with whatever approach you decide to take if you can't figure it out from those hints.
