I´m trying to understand the notion of a stochastic process so I came with the following problem. Let $X$ be a standard normally distributed random variable and form the stochastic process $$Y_{t}=X+2t.$$
For this particular example, I have two questions:
1.- How can I describe the simple paths of the process?
2.- What is the probability that $Y_{t}=0$ for some $t\in \mathbb{N}$?
I´ve never came across with particular examples of stochastic processes, so I hope some illumination with this definitions.
Thank you.