If each observation of a Row data whose variance is $ σ 2 $ is multiplied by $ h $ , then the va

Question

If each observation of a Row data whose variance is $ σ 2 $ is multiplied by $ h $ , then the variance of the new set is

Accepted Answer

The variance of a linear transformation of a random variable follows the rule: $$ Var(ax + b) = a 2 · Var(x) $$ Given that $ a = h $ and $ b = 0 $, we apply this property: $$ Var(h · x) = h 2 · Var(x) $$ Since $ Var(x) = σ 2 $, we get: $$ Var(h · x) = h 2 σ 2 $$

Question 40