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v. t. e. In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability ...
The variance of a random variable is the expected value of the squared deviation from the mean of , : This definition encompasses random variables that are generated by processes that are discrete, continuous, neither, or mixed. The variance can also be thought of as the covariance of a random variable with itself:
Law of total expectation. The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations[2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same ...
Conditional expectation. In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can ...
The expected value and variance of a geometrically distributed ... Substituting this estimate in the formula for the expected value of a geometric distribution and ...
Law of total variance. In probability theory, the law of total variance[1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and are random variables on the same probability space, and the variance of is finite, then. {\displaystyle \operatorname {Var} (Y ...
Cumulative probability of a normal distribution with expected value 0 and standard deviation 1. In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1]
The expected value or mean of a random vector is a fixed vector [] whose elements are the expected values of the respective random variables. [ 3 ] : p.333 E [ X ] = ( E [ X 1 ] , . . .