題組內容

1. (5% each, 20% in total) Yes/No questions. No need to state reasons.

(d) Consider a random variable \( X \). Let random variable \( Y = a \cdot X + b \), for some constants \( a \) and \( b \). Let \( Var[X] \) and \( Var[Y] \) be the variances of \( X \) and \( Y \), respectively. Is the statement "Var[Y] = a · Var[X] + b" true?