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A program’s pseudo-random outputs are reused with the same seed. Does that create new independent evidence each rerun?

Read the idea, work independently, then explain what changed.

TOPIC 01

Probability: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

A program’s pseudo-random outputs are reused with the same seed. Does that create new independent evidence each rerun?

n=80n=80
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Distinguish observed relative frequency from a model probability and describe the experiment.
Hint 2
Inspect whether the sequence actually changes.
Worked solution
  1. Distinguish observed relative frequency from a model probability and describe the experiment.

  2. Calculate or simplify this relation.

    same seed⇒same deterministic sequence\text{same seed}\Rightarrow\text{same deterministic sequence}
  3. Reproducibility is valuable but does not multiply the number of independent runs.

No; reproducing the same sequence repeats the same simulated observations.

Checks and common pitfalls: Reproducibility is valuable but does not multiply the number of independent runs.

Reasoning checklist · self / teacher assessment
  • State the relevant definition, condition or model.
  • Show a valid calculation, proof or counterexample.
  • Interpret the conclusion with its restrictions.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗