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# PDF - Le arning Obje s ctive fine nsity function De...

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Learning Objectives Define probability density function Set up and use the probability density function of continuous random variables.

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Continuous RVs A continuous randomvariableis onewhich takes an infinitenumber of possiblevalues. RV X is continuous if thereis a non-negativefunction (f) such that for every subset (B) of thereal line: PX B ( 29 = f X x (29 B dx
Examples of Continuous RV’s Most measurements arecontinuous RV’s Temperature, time, concentration, distance, and most other physical parameters arecontinuous RV’s Continuous RV’s areoften approximated as discreteRV’s dueto Rounding Digitization

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PDF This function (f), which corresponds to a PMF of a discrete RV, is called theprobability density function or PDF discrete continuous PMF PDF f X x (29 p X x (29
PDF Use to calculate probability that the value of X is in an interval (a,b) Pa X b ( 29 = f X x (29 dx a b

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Area under PDF Interpret area under PDF as probability b a x f(x) Pa X b ( 29 = f X x (29 dx a b Note that f x ( x ) can take on values greater than 1
PMF vs PDF Continuous RV Discrete RV

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