# Thread: Searching for a probability distribution where expected value is zero.

1. ## Searching for a probability distribution where expected value is zero.

Hi,

I am working on an agent based model. And, in the model every agent has an action. The action leads to a certain pay-off. The assumption is that the agent is not aware of all the actions but only the pay-off generated. Hence, in order to know what payoff an action will generate, the agent has to execute the action.

I use normal probability distribution to model the payoffs. Every agent has 100 actions.
Mean = action number, i.e. 1, 2,3,...until 100.
Std. dev = (1 / talent of the agent)

Hence, if an agent is very talented the spread of his normal distribution is small. Now, this fits well logically. However, the problem starts once they start executing the actions. Once the mean is more than 2 then, irrespective of the value of Std.dev the expected value is always positive, i.e. the action always generates a positive payoff. Whereas, I am trying to search for a probability distribution where the random draw generated from a probability distribution is positive or negative with equal probability, in other words where the expected value is zero.

I hope I could explain the issue properly, if somehow that is not the case, please do let me know.

2. ## Re: Searching for a probability distribution where expected value is zero.

Originally Posted by Neha
Hi
Once the mean is more than 2 then, irrespective of the value of Std.dev the expected value is always positive, i.e. the action always generates a positive payoff.
.
Hi,
Unless I completely misunderstand something, this is a perfectly normal behaviour, as the mean of the normal distribution is exactly the expected value. I think, you would need to rethink how you model the payoffs, the mean beeing equal to the action number is modelling a situation where each payoff is larger then the previous one. Was this your intent?

regards

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