Probability-densityFunction The probability density function defines the probability that ameasured variable might assume a particular value upon anyindividual measurement.It also provides the central tendency of the variable and itsvariation.This central tendency is the desired representativevalue that gives the best estimate of the true mean value
Probability-density Function • The probability density function defines the probability that a measured variable might assume a particular value upon any individual measurement. • It also provides the central tendency of the variable and its variation. This central tendency is the desired representative value that gives the best estimate of the true mean value
ProbabilityDensityFunction(2)expO02TO(2Tp(x)p(x)X
Probability Density Function (2)
ProbabilityDensityFunction(3)26x-fora<x≤c(b-a)(c-a)wherea<x<b,otherwisep(x)=012(b -x)b-aforc<x<b(b-a)(b-cp(x)p(x)badaC
Probability Density Function (3)
ProbabilityDensityFunction(4)N!N一1X(N-n)!n!x!p(n)p(x)
Probability Density Function (4)
Mean Value and Variance (1)Regardless of its probability density form, a variable thatshows a central tendency can be described and quantifiedthrough its mean value and variancelimXx(t)dtT-o0T0for any continuous random variable x is equivalent to8xp(x)dx8
Mean Value and Variance (1) Regardless of its probability density form, a variable that shows a central tendency can be described and quantified through its mean value and variance for any continuous random variable x is equivalent to