This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: C. , C2. .CwnCag o S"! whom induct (Law. . WnlLr‘u {we7n 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 (359)
—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(xy)fr(y)dy= f fx.y(x,y>dy (3.1 Figure 3.14 Joint and marginal PDFs of two continuous random variables. ...
View
Full
Document
 Fall '08
 GEHNAM
 Civil Engineering, Probability theory, marginal pdfs, multiple random variables

Click to edit the document details