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Can these numbers be a probability distribution? Explain.

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

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高三選擇性必修第三册(A版).pdf · 7.2 · PDF 61 / printed page 56

Revisit first: Conditional and total probability

TOPIC 01

Discrete random variables and distributions

Construct a distribution and compute event probabilities from its support.

What you will be able to explain

Construct a distribution and compute event probabilities from its support.
Justify the method and check the conditions in a new situation.

Try it. Leave your reasoning visible.

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

01 / Standard#Your turn

Can these numbers be a probability distribution? Explain.

X=0,11,12;\quad P=0.6,0.5,-0.1

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

Check nonnegativity as well as the total.

Worked solution

List the possible values and probabilities before computing moments.
Apply the stated relation and retain its conditions.
$0.6+0.5-0.1=1$
Apply the stated relation and retain its conditions.
$P(X=t+1)=-0.1<0$
A sum of one alone is insufficient.

The requested relation or conclusion is shown below.

\text{invalid}

Checks and common pitfalls: A sum of one alone is insufficient.

Reasoning checklist · self / teacher assessment

State a valid definition or model and its assumptions.
Show the intermediate mathematical relations, not only the final claim.
Check exclusions, units or the interpretation of the result.

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

Teacher preparation and assessment

Question sequence

Construct a distribution and compute event probabilities from its support.
Which condition is essential in discrete random variables and distributions?
Can two different outcomes lead to the same random-variable value?

Board plan

Defining relation: Construct a distribution and compute event probabilities from its support.
$\sum_xP(X=x)=1$
Conditions: Every probability lies in [0,1]; values and events must not be double-counted.

Anticipated thinking

A random variable value and its probability are not interchangeable.

Assessment checklist

1 mark: choose the correct representation and conditions.
1 mark: establish the intermediate relation.
1 mark: complete a connected calculation or proof.
1 mark: interpret and check the conclusion.