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!