Your browser does not currently recognize any of the video formats available. Click here to visit our frequently. Find expected value based on calculated probabilities. The expected value (or mean) of X, where X is a discrete random variable, is a To find E[ f(X) ], where f(X) is a function of X, use the following formula: E[ f(X) ]. Thanks to all authors for creating a page that has been read , times. In decision theory , and in particular in choice under uncertainty , an agent is described as making an optimal choice in the context of incomplete information. Determine the probability of each possible outcome. Basically, all the formula is telling you to do is find the mean by adding the probabilities. The interpretation is that if you play many times, the average outcome is losing 17 cents per play. Es ist jedoch unmöglich, diesen Wert mit einem einzigen Würfelwurf zu erzielen. Given this information, the calculation is straightforward: The odds that you win the season pass are 1 out of Lose your entire investment. Roughly speaking, this integral is the limiting case of the formula for the expected value of a discrete random variable Here is replaced by the infinitesimal probability of and the integral sign replaces the summation sign.