Var(X) = 4. What is Var(3X - 2)?

Random Variables, Expectation & Variance · Question 59 of 68

Question 59

MediumOriginal question

$\text{Var}(X) = 4$ . What is $\text{Var}(3X - 2)$ ?

10

Correct answerYour answer

12

Correct answerYour answer

34

Correct answerYour answer

36

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\text{Var}(aX + b) = a^{2}\,\text{Var}(X)$ : adding a constant does not change the spread, and the multiplier comes out squared.
$\text{Var}(3X - 2) = 9 \times 4 = 36$ .

Worth noting

12 multiplies by 3 instead of $3^{2} = 9$ .

Ten questions from Random Variables, Expectation & Variance, at your own pace.

Ten questions from Random Variables, Expectation & Variance, at your own pace.