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1.3 Statistics

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We now consider a variable X, whose value is uncertain. In statistics, such a variable is called a random variable, or a stochastic variable. A random variable is a variable whose value is subject to variations and cannot be deterministically assessed. In other words, the specific value cannot be predicted with certainty before an experiment. Random variables can take discrete or continuous values. In geophysics, a number of subsurface properties, such as facies types, porosity, or P‐wave velocity, are considered random variables, because they cannot be exactly measured. Direct measurements are also uncertain, and the measurements should be treated as random variables with a distribution that captures the measurement uncertainty.

Seismic Reservoir Modeling

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