Question: is the sum of two independent random variables independent

title: Sum of normally distributed random variables
text: φ ( t ) = exp ⁡ ( i t μ + σ 2 i 2 t 2 2 ) . ( \ displaystyle \ varphi ( t ) = \ exp \ left ( it \ mu + ( \ sigma ^ ( 2 ) i ^ ( 2 ) t ^ ( 2 ) \ over 2 ) \ right ) . )