Expectation and Variance are fundamental concepts in probability and statistics. The expectation (or expected value) of a random variable represents its theoretical average over an infinite number of trials, essentially summarizing the central tendency of its probability distribution. It is calculated as the weighted sum of all possible values of the variable, where the weights are their respective probabilities. Variance, on the other hand, measures the dispersion or spread of the random variable around its expectation. It quantifies how much the values deviate, on average, from the mean, and is calculated as the expected value of the squared differences between the variable and its mean. Together, expectation and variance provide a comprehensive understanding of a random variable’s behavior, highlighting both its central value and the variability around it.