I'm working on a programming problem that has a very interesting mathematical challenge underneath. I'm given a series of sums of data in timeseries, for example:
$20k between 01.01.2022 and 01.03.2022
$16k between 01.04.2022 and 15.05.2022
$12k between 01.02.2022 and 10.04.2022
Now, I want to create a dataset of the MOST LIKELY numbers for each day, given these sums. The assumption is that this data is normally distributed. The resulting dataset has to sum back to the original given sums.
Some images for examples: Visual example
How would you approach solving this problem?