An unbiased die is thrown $n+2$ times. After each throw a ' + ' is recorded for 2 or 5 and '-' is recorded for $1,3,4$ or 6 , the signs forming an ordered sequence. To each, except the first and last sign, a random variable $X_{i} ; \mathrm{i}=1,2, \ldots, \mathrm{n}$ is associated which takes the value 1 if both of its neighbouring sign differs from the one between them and 0 otherwise. If the random variable $Y$ is defined as $Y=a S+b$ where, $S=\sum_{i=1}^{n} X_{i}$
Which of the following statement(s) is/are true?
A. $V(Y)=a^{2} V(S)$
B. $V(Y) \neq a^{2} V(S)$
C. $E(Y)=a^{2} E(S)+b$
D. $E(Y)=a E(S)+b$
