So this is how we might have, if we had some way, which we have not yet talked about of constructing or sampling from distribution, how we might use those samples for approximating various properties, relative to the distribution p, whether it's a probability of an event or the expectation of a function and know by the way that the expectation of the function subsumes the probability of an even because you can also take the expectation for example an indicator function, and that correspond directly. 