I would like to show (demonstrate by simulation) a random process that turns out after $i$ interactions to be deterministic, i.e. ends at predefined value (roughly) known at time $t=1$.
Conditions for the solution:
1) The random process should display randomness visible (graph) =
2) The "convergence" to the end result should be gradual and therefore the end result surprising to the observer.
3) Solution in R (hopefully).
The meaning of surprising in this case: I mean, during the generating process, the observer expectation is not (rational?) .... (Surprise in sense of conviction that random is not random after all).
Does it matter whether the terminal (final) value is revealed to observer a priori (at the beginning of the generating process series) or after the process ends (to confirm the values match)?
1) If solution is not provided, how to approach it? (any hint helps)
2) Which tool (statistical/modeling) should be used? How to set up the process?
EDIT: improved version (of what I'm asking)
Simulate a (large) number of identically distributed but dependent random variables, such that their sum is ideally equal to a prespecified value, or failing that (for continuous RVs, we will hit a single number with probability 0), which is in a given range with a given probability. (with @Stephan kind help.)