how to find moment generating function of normal distribution
Moment-generating function
M S n ( t ) = M X 1 ( a 1 t ) M X 2 ( a 2 t ) ⋯ M X n ( a n t ) . ( \ displaystyle M_ ( S_ ( n ) ) ( t ) = M_ ( X_ ( 1 ) ) ( a_ ( 1 ) t ) M_ ( X_ ( 2 ) ) ( a_ ( 2 ) t ) \ cdots M_ ( X_ ( n ) ) ( a_ ( n ) t ) \ , . )
M S n ( t ) = M X 1 ( a 1 t ) M X 2 ( a 2 t ) ⋯ M X n ( a n t ) . ( \ displaystyle M_ ( S_ ( n ) ) ( t ) = M_ ( X_ ( 1 ) ) ( a_ ( 1 ) t ) M_ ( X_ ( 2 ) ) ( a_ ( 2 ) t ) \ cdots M_ ( X_ ( n ) ) ( a_ ( n ) t ) \ , . )