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) = `interactive`

**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). 

**Sub-question (setup):**

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)?

**Summary:**

**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)

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> 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.)
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