How to use Ito process at certain time t as a random variable?

Questions
, ,
1

For instance, if I define
process1 = WienerProcess[.3, .5],

I want to get the distribution of this process at time t and then use it as a random variable in the future. I tried to use
dist=process1[t], but it doesn’t work. is there a way that I can get the CDF directly instead of deriving it by myself?

Thanks.

2

would something like

CDF[WienerProcess[.3, .5][t], s]

work?