Probability distributions can exist without a defined mean, as demonstrated by specific series. The exercise presented involves finding a series where the sum converges to 1, qualifying it as a probability distribution, while the weighted sum diverges, indicating the absence of a mean. An example provided is the series defined by a_k = 1/k², which converges but does not yield a finite mean. This illustrates the concept of distributions that lack a mean, challenging traditional notions of probability.
PREREQUISITESMathematicians, statisticians, students of probability theory, and anyone interested in advanced concepts of probability distributions.