# Thread: Probability distribution on next draw from random variable

1. ## Probability distribution on next draw from random variable

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. I am looking to solve for two different probability functions, though I think the math should be very similar:
1. Say there is some random variable . You observe a draw from this distribution, call it , but you do not know . Given , what is the probability that another draw, , from the same distribution, will be greater than or equal to an arbitrary number ? That is, what is:

2. (Note: these problems are separate, so, for example, here does not mean the same thing as in part 1). Say that and are two independent draws from , the standard uniform distribution. Now, and . You observe one draw from and one draw from , but you do not know the true values or . What is the probability that a new draw from will be greater than a new draw from ? That is, if is your observed draw from and is your observed draw from , then what is:

Any help with this would be much appreciated! I've read a bit about convolutions and posterior predictive distributions, but I don't have the grasp on them that I need to solve for these functions.

Thanks!

2. ## Re: Probability distribution on next draw from random variable

This was stuck in the moderator queue and I just saw it. Do you still want help with this?

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