Remember that if we integrate from -o∞ to oo with respect to both variables, the probability should be 1. 1 O 1. The joint density function for a pair of ran- %3D 216 dom variables X and Y is O 2. C = 220 0

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Remember that if we integrate from -oo to oo with respect to both variables, the probability should be 1.
The joint density function for a pair of ran-
dom variables X and Y is
1
C =
216
O 1.
1
O 2. C =
220
f(x, y) = {Cx(1+y) 0 <x< 6,0 < y< 4
otherwise
Į Cr(1+y) 0 <x < 6,0< y < 4
1
C =
209
O 3.
1
C =
223
O 4.
Find the value of the constant C.
1
O 5. C =
208
Transcribed Image Text:Remember that if we integrate from -oo to oo with respect to both variables, the probability should be 1. The joint density function for a pair of ran- dom variables X and Y is 1 C = 216 O 1. 1 O 2. C = 220 f(x, y) = {Cx(1+y) 0 <x< 6,0 < y< 4 otherwise Į Cr(1+y) 0 <x < 6,0< y < 4 1 C = 209 O 3. 1 C = 223 O 4. Find the value of the constant C. 1 O 5. C = 208
Use the transformation (x, y) → (u, v) with
O 1. I =
487
x = 4u,
O 2. I
12
= 3v
O 3. I
127
to evaluate the integral
O 4. I
48
I
2² dxdy
O 5. I =
3
R.
O 6. I =
when R is the region bounded by the ellipse
= 1.
9
16
+
Transcribed Image Text:Use the transformation (x, y) → (u, v) with O 1. I = 487 x = 4u, O 2. I 12 = 3v O 3. I 127 to evaluate the integral O 4. I 48 I 2² dxdy O 5. I = 3 R. O 6. I = when R is the region bounded by the ellipse = 1. 9 16 +
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