LEARN · EXPLAIN · REVISE

Find Var(3X+2).

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

TOPIC 01

Random variables and distributions: mixed review

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

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

01 / Standard#Your turn

Var(X)=27

Variance is nonnegative; variance of a sum includes covariance unless independence is justified.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List the possible values and probabilities before computing moments.

Hint 2

Use this intermediate relation.

Var(aX+b)=a^2Var(X)

Worked solution

The requested value is 243.

Checks and common pitfalls: A constant shift has no effect on variance.

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

Teacher preparation and assessment