### A pedagogical example

- School model:
- three-year third level school
- interesting outputs
- sizes x
_{i}(k) of class i
- number of graduates x
_{g}(k)

- all taken at the beginning of year k
- three versions of growing complexity

- Version A:
- deterministic
- constant fraction R
_{i} of repeaters
- constant fraction D
_{i} of dropouts

- non-integer sizes ("mean values")
- exact definition

- Version B:
- non-deterministic, integer results
- random number of repeaters ξ
_{R,i} and
dropouts ξ_{D,i}
- given by binomial distribution B(n,p)
- model equations change by

- Version C:
- add a fraction M
_{i} of pupils, who downgrade
at midterm
- number of pupils again binomial
- ξ
_{M,i} ~ B(x_{i}(k), M_{i})

- change from sample time 1 to mixed sample times!