[Community Question] Statistics: Find skewed standard distribution given the mean and bounds for the other values

One of our user asked:

I am working on a project but need to find a skewed standard distribution, and we can't figure out how.

We have two variables: $p$, which is a probability and $PV$ which is an integer variable between 0 and 10 There are two demands that need to be meeted:

1. The mean must lay at $PV \cdot p$
2. The values with non-zero probability must lay between 0 and PV.

Is it possible to accomplish this? And how? (If somebody has a tip how to implement it in Python, let me know)