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The mathematical expectation is denoted by the formula: E (X)= Σ (x 1 p 1, x 2 p 2, …, x n p n ), where, x is a random variable with the probability function, f (x), p is the probability of the occurrence, and n is the number of all possible values.
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.
The expected value in statistics is the long-run average outcome of a random variable based on its possible outcomes and their respective probabilities. Essentially, if an experiment (like a game of chance) were repeated, the expected value tells us the average result we’d see in the long run.
Expected value (= mean=average): Definition. Let X be a discrete random variable with range RX = {x1,x2,x3,... } (finite or countably infinite). The expected value of X, denoted by EX is defined as. EX = ∑xk∈RX xkP(X = xk) = ∑xk∈RX xkPX(xk).
Properties of the expected value. by Marco Taboga, PhD. This lecture discusses some fundamental properties of the expected value operator. Some of these properties can be proved using the material presented in previous lectures.
Expected value uses probability to tell us what outcomes to expect in the long run. Problem 1: Board game spinner. A board game uses the spinner shown below to determine how many spaces a player will move forward on each turn. The probability is 1 2 that the player moves forward 1 space, and moving forward 2 or 3 spaces each have 1 4 probability.
Expected Value: If O O represents an outcome of an experiment and n(O) n ( O) represents the value of that outcome, then the expected value of the experiment is: ∑n(O) × P(O) ∑ n ( O) × P ( O) , where Σ Σ is the “sum,” meaning we add up the results of the formula that follows over all possible outcomes.
Calculate probabilities and expected value of random variables, and look at ways to ransform and combine random variables. A random variable is some outcome from a chance process, like how many heads will occur in a series of 20 flips, or how many seconds it took someone to read this sentence.
The expected value is a weighted average of the possible realizations of the random variable (the possible outcomes of the game). Each realization is weighted by its probability.
In probability theory, an expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment. Expected value is a measure of central tendency; a value for which the results will tend to.
