Match List-I with List-II. The probability distribution of number of sixes(X) is when an unbiased die is thrown twice is :

Choose the correct answer from the options given below :

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A) $E(X)=∑XP(X)$

$=0×\frac{25}{36}+1×\frac{5}{18}+2×\frac{1}{18}$

$=\frac{12}{13}=\frac{1}{3}$

(B) $E(X^2)=0^2×\frac{25}{36}+1^2×\frac{5}{18}+2^2×\frac{1}{36}$

$=\frac{7}{18}$

$Var(X)=E(X^2)-[E(X)]^2$

$=\frac{7}{18}-\left(\frac{1}{3}\right)^2=\frac{5}{18}$

(C) $Var(aN)=a^2\,Var(N)$

$⇒Var(\frac{X}{2})=\left(\frac{1}{2}\right)^2Var(X)=\frac{1}{4}×\frac{5}{18}$

$=\frac{5}{72}$

(D) $E(\frac{3}{8}X)=\frac{3}{8}E(X)$

$=\frac{3}{8}×\frac{1}{3}=\frac{1}{8}$