The one-dimensional distribution of a stochastic process \(\{X(t), t>0\}\) is

\[F_{t}(x)=P(X(t) \leq x)=\frac{1}{\sqrt{2 \pi t} \sigma} \int_{-\infty}^{x} e^{-\frac{(u-\mu)^{2}}{2 \sigma^{2} t}} d u\]

with \(\mu>0, \sigma>0 ; x \in(-\infty+\infty)\).

Determine its trend function \(m(t)\) and, for \(\mu=2\) and \(\sigma=0.5\), sketch the functions

\[y_{1}(t)=m(t)+\sqrt{\operatorname{Var}(X(t))} \quad \text { and } \quad y_{2}(t)=m(t)-\sqrt{\operatorname{Var}(X(t))}\]