Mathematical expectation of a discrete and continuous random variable x.
Because random variables are random, knowing the outcome on any one realization of the random process is not possible. Instead, we can talk about what we might expect to happen, or what might happen on average.
This is the idea of mathematical expectation. In more usual terms, the mathematical expression of the probability distribution of a random variable is the mean of the random variable. Mathematical expectation goes far beyond just computing means, but we begin here as the idea of a Mean is easily understood. #mathematics #statistics #expectations #probability #mean #random #continuous #pdf #cdf #probabilitytheory