Another Standard Deviation Question (event frequency)

[QuadsOverQuads]

Say I have three events with the following expected average frequencies:

Event 1 : 1-per-5000 hands
Event 2 : 1-per-7500 hands
Event 3 : 1-per-12000 hands

These events are mutually exclusive and independent.

I can calculate the average frequency at which any one of these events will occur in a given hand (not difficult).

However, now I need to calculate the standard deviation of that event-frequency, to determine a 95% confidence interval (2-sigma). The reason is, I'm actually looking at a progressive jackpot structure, and the actual jackpot size is not fixed, but varies depending on how frequently the jackpot hits. I want to put a low and a high expectation on the jackpot size at the time it hits, and that brings me back to the expected event frequency and its standard deviation.

I generally understand SD for probabilities (thanks to much assistance from this forum!), but this new problem is confusing me.

If anyone has any simple explanation or pointers to resources on this subject, it would be greatly appreciated.


q/q

[DrVanNostrin]

The events can't be mutually exclusive and indepentant. Being indepentant means P(A|B) = P(A). Being mutually exclusive means P(A|B) = 0.

The number of hands until the JP is hit should follow a geometric distribution.