Kenneth ChengMathematical modeling
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Find P(X≥t).

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

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TOPIC 01

Random variables and distributions: mixed review

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

Find P(X≥t).

X∈{0,21,22};P=(1/4,1/4,1/2)X\in\{0,21,22\};\quad P=(1/4,1/4,1/2)
  • Every probability lies in [0,1]; values and events must not be double-counted.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
List the possible values and probabilities before computing moments.
Hint 2
Add probabilities at t and t+1.
Worked solution

  1. List the possible values and probabilities before computing moments.

  2. Apply the stated relation and retain its conditions.

    P(X≥t)=1/4+1/2=3/4P(X\ge t)=1/4+1/2=3/4

  3. The threshold selects values, then their probabilities are added.

The requested value is 0.75.

Checks and common pitfalls: The threshold selects values, then their probabilities are added.

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 ↗