Example - University of Texas at Dallassaquib/ENGR3341/Chap6-7/Chapter6-7-ppt.pdfChapter 6...
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Transcript of Example - University of Texas at Dallassaquib/ENGR3341/Chap6-7/Chapter6-7-ppt.pdfChapter 6...
Example
Example
Jointly Gaussian Random Variabl• X and Y have a bivariate Gaussian PDF if
f X , Y (x, y) =
exp− σ 1
.x−µ1
. 2 − 2ρ(x−µ1 ) (y−µ2 )σ 1σ 2
+ σ 2
2(1 −ρ2)
.y−µ2
. 2
2πσ1σ2,1 −ρ2
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σ1 > 0, σ2 > 0, −1 ≤ ρ ≤ 1
ρ = 0
0.35
0.3
0.25
0.2
0.15
0.1
0.05
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0
21
0-1
-2-3
3 3x
y
f X , Y (x, y)
• µ1 = µ2 = 0 • σ1 = σ2 = 1
