CE408_Lecture_15_101111

CE408_Lecture_15_101111 - C. , C2. .CwnCag o S"!...

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Unformatted text preview: C. , C2. .CwnCag o S"! whom induct (Law. . WnlLr‘u {we-7n 9! 3 . MAW? 01g £91314)- %D+ ,4 W! 4‘39; '3ng ed ?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 (3-59) —00 -oo 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(x|y)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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CE408_Lecture_15_101111 - C. , C2. .CwnCag o S&amp;quot;!...

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