Re: Probability Density Function

*To*: mathgroup at smc.vnet.net*Subject*: [mg74807] Re: [mg74790] Probability Density Function*From*: Darren Glosemeyer <darreng at wolfram.com>*Date*: Fri, 6 Apr 2007 04:18:09 -0400 (EDT)*References*: <200704050812.EAA20924@smc.vnet.net>

Tony Harris wrote: > Hello, > > I have graphed a normal probability density function with a mean of 10 and a > standard deviation of 2.5. I named this function f[x] > > I wanted to know how to use the "FilledPlot" to show the area under the > curve for (x<8) and (7.5<x<11). > > I have the probability for x<8 to be .212 and for 7.5<x<11 to be .497 by > calculating the definite integral of the function f[x] for these two > probabilities. > > I have the cacluation of the probabilities included but no idea on how to > continue and display each of these in a graph. > > Thanks, > > T Harris > > This can be accomplished by plotting the pdf and the pdf multiplied by a Piecewise function which is 1 for the desired region and 0 otherwise and filling from the Piecewise function to the axis. This will illustrate the probability that x<8. FilledPlot[PDF[NormalDistribution[10, 2.5], x]*{1, Piecewise[{{1, x < 8}}]}, {x, 0, 20}, Fills -> {{{2, Axis}, Red}}] Likewise, this will show the probability for 7.5<x<11. FilledPlot[PDF[NormalDistribution[10, 2.5], x]*{1, Piecewise[{{1, 7.5 < x < 11}}]}, {x, 0, 20}, Fills -> {{{2, Axis}, Red}}, PlotPoints -> 20] The two regions can be shown in the same plot if desired. FilledPlot[PDF[NormalDistribution[10, 2.5], x]*{1, Piecewise[{{1, x < 8}}], Piecewise[{{1, 7.5 < x < 11}}]}, {x, 0, 20}, Fills -> {{{2, Axis}, Red}, {{3, Axis}, Blue}}, PlotPoints -> 20] However, there is some overlap in these two regions. A fourth function for the overlap region, as in the following, could be used to show this. FilledPlot[PDF[NormalDistribution[10, 2.5], x]*{1, Piecewise[{{1, x < 8}}], Piecewise[{{1, 7.5 < x < 11}}], Piecewise[{{1, 7.5 < x < 8}}]}, {x, 0, 20}, Fills -> {{{2, Axis}, Red}, {{3, Axis}, Blue}, {{4, Axis}, Purple}}, PlotPoints -> 50] Darren Glosemeyer Wolfram Research

**References**:**Probability Density Function***From:*"Tony Harris" <tdh1967@bellsouth.net>