Propergate Up Tree: Average Level 2

• average across all programs to get average M₂
• function's argument may be either leaf or tree of height one.

  leaf

  probability vector =u₀. Chance of leaf =p'₀₀

  function

  probability vector is the same as in the longest path So u'₁ = u₁ = u₀ M₁.

  Chance of function =p'₂₀

• M₂ = p'₀₀ u₀N + p'₂₀ u₁N.

  Note since $u_1 \not= u_0$, $M_2 \not= M_1, \Rightarrow$ not Markov.