I didn't quite understand what you meant by "on the basis of an external event." But you can certainly flip a fair coin in a manner that a remote user can cryptographically verify.
Consider this algorithm:
- Bob picks a uniformly random boolean value, TRUE or FALSE. He also chooses a large random number. He sends Alice the SHA-256 hash of the boolean value concatenated with the number. (E.g. he sends the hash of "TRUE|12345678".) Since Alice doesn't know the random number and the hash is one-way, Alice doesn't know the boolean value.
- Alice flips a coin and sends Bob the value -- TRUE or FALSE.
- Bob reveals the random number, and thus his own boolean value. Alice verifies that the boolean value and the random number indeed hash to the value she received earlier.
- This final output of the coin flip is the exclusive-or of Alice's boolean value and Bob's boolean value.
With this algorithm, no party can cheat without the cooperation of the counterparty. If either party plays fairly, the output will be a uniform random boolean value.
(EDIT) I now understand the problem to mean you have no internal source of nondeterminism at all, so all randomness has to come from an external source and the algorithm has to be deterministic. In that case, we can still use cryptography to help.
How about taking the SHA-256 of the PDF version of The New York Times every day, or the SHA-256 of the volume and closing price of all the stocks in the Dow Jones Industrial Average in alphabetical order by ticker symbol, or really the secure hash of anything that can be mutually observed and that you can't influence. If you want just one bit, take the first bit of the SHA-256.
If you want a normal distribution, you could take the whole thing in two parts (128 bits, then 128 bits) as two uniform deviates and use the Box-Muller transform to get two normal deviates.