Re: drawing realizations from a joint PDF

• To: mathgroup at smc.vnet.net
• Subject: [mg3515] Re: drawing realizations from a joint PDF
• From: Jorma Virtamo <jorma.virtamo at vtt.fi>
• Date: Wed, 20 Mar 1996 02:49:14 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```deb at Alceon.com (David E. Burmaster) wrote:

>I have a bivariate random variable described by this PDF
>
>        f(x, y) = x + y         for 0 <= x <= 1 AND 0 <= y <= 1
>
>In Mma, how can I draw realizations from the joint PDF??

Try this one:

r := Random[]
z := Module[ {x,y},
x = Sqrt[.25 + 2r] - .5;
y = Sqrt[x^2 + (1+2x)r] - x;
Return[{x,y}] ]

You can visualize a realization of 5000 points by

Show[ Graphics[{PointSize[.01], Point /@ Table[z,{5000}]}],
PlotRange->{{0,1},{0,1}},
AspectRatio->1,
Frame->True ];

-- Jorma Virtamo

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Jorma Virtamo                      VTT Information Technology
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fax:   +358 0 455 0115             P.O. Box 1202
email: jorma.virtamo at vtt.fi        FIN-02044 VTT
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