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?a(YébcL\/éd = 4 z oldie 3.3 Multiple Random Variables . 133 fX.Y(x.W Surface {(x, y) Figure 3.13 Volume under the PDF f xly(x,y). Then,
I y
Fx.r(x. y) =f f fx.r(u,v)dvdu (359)
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Conversely, if the partial derivatives exist,
azFX Y(xa l = _——' 3.60
fx,r(x y} axay ( ) Also, we observe the following probability: b d
P(a < X s b,c < Y 5 d) =f [ fx_y(u, v)dvdu
a C which is the volume under the surface f(x, y) as shown in Fig. 3.13. Manhood; wa. Disi‘u‘b. pound. . x =b‘w F): (1")
2—390 PM“): «Um Fx,(x.‘15 Finally, through the theorem of total probability, we obtain the marginal PDFs, mac): f fxly(xy)fr(y)dy= f fx.y(x,y>dy (3.1 Figure 3.14 Joint and marginal PDFs of two continuous random variables. ...
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 Fall '08
 GEHNAM
 Civil Engineering, Probability theory, marginal pdfs, multiple random variables

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