$Y \sim N(a\mu + b, a\sigma^2)$

$Y \sim N(a\mu + b, a^2\sigma^2)$

The characteristic function of $Y$ is $\exp(it(a\mu+b) - \frac{1}{2}a^2\sigma^2 t^2)$

The characteristic function of $Y$ is $\exp(it(a\mu+b) - \frac{1}{2}a\sigma^2 t^2)$