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Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
The following graph displays the expected value taking uncertainty into account (the smooth blue curve) to the expected utility ignoring uncertainty, graphed as a function of the decision variable. When uncertainty is ignored, one acts as though the flight will be made with certainty as long as one leaves at least 100 minutes before the flight ...
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure
A project value is computed for each scenario, and the expected commercial value is obtained by multiplying each situation's value by the scenario odds and adding the results. Depending on the procedures used to estimate the value of the project under each scenario, ECV can be a useful way to address project uncertainties.
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. [1] It is calculated by using the following formula:
This special case is how expected value of perfect information and expected value of sample information are calculated where risk neutrality is implicitly assumed. For cases where the decision-maker is risk averse or risk seeking , this simple calculation does not necessarily yield the correct result, and iterative calculation is the only way ...
Expected value of sample information, the expected increase in utility that a decision-maker could obtain from gaining access to a sample of additional observations before making a decision Expected value of including uncertainty , the expected difference in the value of a decision based on a probabilistic analysis versus a decision based on an ...