Q23Multiple correct3 Marks6 Aug 2023Suppose X1,X2,X3,X4∼i.i.d. XX_1,X_2,X_3,X_4\sim \text{i.i.d. }XX1,X2,X3,X4∼i.i.d. X with E[X]=10E[X]=10E[X]=10 and Var(X)=4\operatorname{Var}(X)=4Var(X)=4. Define S=2X1−2X2−X3+3X4S=2X_1-2X_2-X_3+3X_4S=2X1−2X2−X3+3X4. Choose the correct option(s) from below:AE[S]=20E[S]=20E[S]=20BVar(S)=52\operatorname{Var}(S)=52Var(S)=52CVar(S)=72\operatorname{Var}(S)=72Var(S)=72DE[S]=180E[S]=180E[S]=180
