Connect precedence proofs, combinatorial sample spaces and dependent indicators. Use targeted returns to matching, orders, planarity and modular arithmetic without requiring whole advanced courses.
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Feasibility, elapsed time and worker constraints are different claims.
It orders prerequisites before dependents. Optimal elapsed time additionally needs durations and a resource model; unlimited-worker earliest finishes need not form a feasible schedule with a worker limit.
Sampling without replacement commonly creates dependence.
No. For finite random quantities, expanding the finite weighted sums proves E[X+Y]=E[X]+E[Y]. Independence is needed for a general product factorization, not this sum rule.
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Changed constraints and random precedence
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Build earliest schedules, prove their optimality and diagnose the resource assumptions behind the proof.
8 practice tasks.
Build a finite probability model, add indicator expectations without independence, and sharpen a tail bound using pairs of events.
6 practice tasks.
