Question

If \(Y=20+10X\), then \(Var[Y]\) is

• A. 100 · Var[X]
• B. 10 · Var[X]
• C. 400 + 100 · Var[X]
• D. 20 + 10 · Var[X]

Hint:

Variance is unaffected by constant additions (like 20), but scaling the variable (like 10X) squares the constant (10).

Answer 1

The Correct Option is A

Given that \(Y = 20 + 10X,\) the variance of Y is calculated as:
\( Var(Y)=102Var(X)=100Var(X)\)

Consequently, option (a) is the correct answer.