LEARN · EXPLAIN · REVISE

Give the distribution of Y=2X+1.

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

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

TOPIC 01

Discrete random variables and distributions

Construct a distribution and compute event probabilities from its support.

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

01 / Standard#Your turn

X=0,9;\quad P=1/3,2/3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List the possible values and probabilities before computing moments.

Hint 2

Map each support value through Y=2X+1.

Worked solution

List the possible values and probabilities before computing moments.
Apply the stated relation and retain its conditions.
$0\mapsto1,\quad 9\mapsto19$
An injective value transformation keeps the corresponding probabilities.

The requested relation or conclusion is shown below.

Y=1,19;\quad P=1/3,2/3

Checks and common pitfalls: An injective value transformation keeps the corresponding probabilities.

Reasoning checklist · self / teacher assessment

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

Teacher preparation and assessment

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.