In words, the variance of a random variable is the average of the squared deviations of the random variable from its mean (expected value). The standard deviation is interpreted as a measure of how "s...In words, the variance of a random variable is the average of the squared deviations of the random variable from its mean (expected value). The standard deviation is interpreted as a measure of how "spread out'' the possible values of X are with respect to the mean of X, μ=E[X]. Continuing in the context of flipping a coin, we calculate the variance and standard deviation of the random variable X denoting the number of heads obtained in two tosses of a fair coin.
This page explains variance and standard deviation as essential features of random variables. Variance represents the average of squared deviations from the mean, while standard deviation, the square ...This page explains variance and standard deviation as essential features of random variables. Variance represents the average of squared deviations from the mean, while standard deviation, the square root of variance, enhances interpretation. The text includes calculations and practical examples, such as coin flips, along with important theorems about variance's non-linearity and how linear transformations impact it. It also mentions that shifting a random variable does not change its variance.
