Given a discrete series of random variable $n(i)$ that each element follows the standard normal distribution $N(0,1)$, another series is defined iteratively as: $$u(i+1)=au(i)+bn(i)$$ where $0<a<1$ and $b$ any real number.
How to show that $u$ is also a normal-distributed random variable?
What is the variance of $u$ in terms of $a$ and $b$?
Thanks.