(5) A bivariate density is-{**Sx² y², if x € (-1, 1), 0 < y < x²f(x, у) :%3Dotherwise.The marginal densities of X and Y arefx(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 is3x2if 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 is3x2if 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 isЗу?{;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 is3y?2(1+y3/2)if y < x? < 1,fx\Y=y (x) =otherwise.(e) None of the aboveThe correct answer is(a)(b)(c)(d)(e)N/A(Select One)

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(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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(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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