Re: Probability Density Function

• To: mathgroup at smc.vnet.net
• Subject: [mg74817] Re: Probability Density Function
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Fri, 6 Apr 2007 04:23:17 -0400 (EDT)
• References: <ev2beo\$kl0\$1@smc.vnet.net>

```On Apr 5, 1:19 am, "Tony Harris" <tdh1... at bellsouth.net> 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

<< Graphics`FilledPlot`

f[x_,m_,s_] := Exp[-.5((x-m)/s)^2]/(s*Sqrt[2Pi])

FilledPlot[{f[x,10,2.5],f[x,10,2.5]*UnitStep[8-x]},{x,0,20},
Fills->{{{2,Axis},GrayLevel[.75]}}];

FilledPlot[{f[x,10,2.5],f[x,10,2.5]*UnitStep[(x-7.5)(11-x)]},{x,
0,20},
Fills->{{{2,Axis},GrayLevel[.75]}}];

```

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