(5) A bivariate density is Sx? y², if x € (-1, 1), 0 < y < x² f(x, y) := otherwise. The marginal densities of X and Y are 9. fx(x) = 5**, x€ (-1, 1); frv) = 9y°(1 – y2), 0 < y < 1. Obtain the conditional density fxIY=y (x).
(5) A bivariate density is Sx? y², if x € (-1, 1), 0 < y < x² f(x, y) := otherwise. The marginal densities of X and Y are 9. fx(x) = 5**, x€ (-1, 1); frv) = 9y°(1 – y2), 0 < y < 1. Obtain the conditional density fxIY=y (x).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
100%
![(5) A bivariate density is
-{**
Sx² y², if x € (-1, 1), 0 < y < x²
f(x, у) :%3D
otherwise.
The marginal densities of X and Y are
fx(x) =
**, xE (-1, 1);
fr(v) = 9y²(1 – y³2),
0 < y < 1.
Obtain the conditional density fx|Y=y(x).
The following answers are proposed.
(a) For y E (0, 1), the conditional density of X given Y = y is
3x2
if y < x² < 1,
fx\Y=y (x) =
2(1-y3/2)
otherwise.
(b) For y E (x², 1), the conditional density of X given Y = y is
3x2
if 0 < y < 1,
fx\Y=y (x) =
2(1-y3/2)
otherwise.
(c) For y E (x², 1), the conditional density of X given Y = y is
Зу?
{;
if 0 < y < 1,
fx\Y=y (x) =
2(1+y3/2)
otherwise.
(d) For y E (0, 1), the conditional density of X given Y = y is
3y?
2(1+y3/2)
if y < x? < 1,
fx\Y=y (x) =
otherwise.
(e) None of the above
The correct answer is
(a)
(b)
(c)
(d)
(e)
N/A
(Select One)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6214fda8-f992-4e88-b320-5195339361f5%2F9d08a7ed-1de7-4354-89bc-1743c8f6dddb%2Flipnam_processed.png&w=3840&q=75)
Transcribed Image Text:(5) A bivariate density is
-{**
Sx² y², if x € (-1, 1), 0 < y < x²
f(x, у) :%3D
otherwise.
The marginal densities of X and Y are
fx(x) =
**, xE (-1, 1);
fr(v) = 9y²(1 – y³2),
0 < y < 1.
Obtain the conditional density fx|Y=y(x).
The following answers are proposed.
(a) For y E (0, 1), the conditional density of X given Y = y is
3x2
if y < x² < 1,
fx\Y=y (x) =
2(1-y3/2)
otherwise.
(b) For y E (x², 1), the conditional density of X given Y = y is
3x2
if 0 < y < 1,
fx\Y=y (x) =
2(1-y3/2)
otherwise.
(c) For y E (x², 1), the conditional density of X given Y = y is
Зу?
{;
if 0 < y < 1,
fx\Y=y (x) =
2(1+y3/2)
otherwise.
(d) For y E (0, 1), the conditional density of X given Y = y is
3y?
2(1+y3/2)
if y < x? < 1,
fx\Y=y (x) =
otherwise.
(e) None of the above
The correct answer is
(a)
(b)
(c)
(d)
(e)
N/A
(Select One)
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