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:<math>P(a \leq x \leq b) = \int_a^b f(x) \, dx </math>
 
:<math>P(a \leq x \leq b) = \int_a^b f(x) \, dx </math>
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This density function is intended to express mathematically the total apportionment of the values of the variable it represents over its entire [[domain]].  It is necessary to express probability this way for a variable or parameter which may take on a continuum of values, so that the total probability covering the entire domain of support may converge to a finite value.  The counterpart for a discretely distributed variable is the [[probability mass function]].
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This density function is intended to express mathematically the total apportionment of the values of the variable it represents over the variables entire [[domain]].  It is necessary to express probability this way for a variable or parameter which may take on a continuum of values so that the total probability covering the entire domain of support may converge to a finite value.  The counterpart for a discretely distributed variable is the [[probability mass function]].
    
In order to qualify, such a function must meet the following criteria:
 
In order to qualify, such a function must meet the following criteria:
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