Thus, for a continuous random variable the expected value is the limit of the weighted sum, i.e. Since probability can never be negative (although it can be zero), one can intuitively understand this as the area under the curve of the graph of the values of a random variable multiplied by the probability of that value. The weights used in computing this average are the probabilities in the case of a discrete random variable (that is, a random variable that can only take on a finite number of values, such as a roll of a pair of dice), or the values of a probability density function in the case of a continuous random variable (that is, a random variable that can assume a theoretically infinite number of values, such as the height of a person).ДЇrom a rigorous theoretical standpoint, the expected value of a continuous variable is the integral of the random variable with respect to its probability measure.

In other words, each possible value the random variable can assume is multiplied by its assigned weight, and the resulting products are then added together to find the expected value.

More formally, the expected value is a weighted average of all possible values. In probability theory, the expected value refers, intuitively, to the value of a random variable one would вЂњexpectвЂќ to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained.

weighted average: an arithmetic mean of values biased according to agreed weightings.

integral: the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.

random variable: a quantity whose value is random and to which a probability distribution is assigned, such as the possible outcome of a roll of a die.

From a rigorous theoretical standpoint, the expected value of a continuous variable is the integral of the random variable with respect to its probability measure.

The intuitive explanation of the expected value above is a consequence of the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as the sample size grows to infinity.

Enter numbers in correct format 'Scientific' format is acceptable (the maximum exponent 99 as in regular. This calculator simplifies the calculus by making the most common operations automatically. The expected value refers, intuitively, to the value of a random variable one would вЂњexpectвЂќ to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained. In other words, you want to know how the standard deviation of the primary parameter(s) propagates to the resulting parameter.

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