Please answer both. Thank you! (5) Consider the joint p.d.f. of continuous random variables X and Y:f(x,y) = {1, y (4) The joint p.d.f of the random variables X and Y is1½, x² + y² >1,f(x, y) =-{(b) P(X² +Y² < ½).0,otherwise.Find(a) P[(X,Y) € A], where A is the sector of the unit circle in the first quadrantbounded by y = 0 and y = x

Answered: (5) Consider the joint p.d.f. of…

Math

Statistics

(5) Consider the joint p.d.f. of continuous random variables X and Y 1, y

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Question

Please answer both. Thank you!

(5) Consider the joint p.d.f. of continuous random variables X and Y:
f(x,y) = {
1, y<x<y+1 and 0 ≤ y ≤ 1,
0, otherwise.
(a) Find the marginal p.d.f. of X.
(b) Find the marginal p.d.f. of Y.

(4) The joint p.d.f of the random variables X and Y is
1
½, x² + y² >1,
f(x, y) =
-{
(b) P(X² +Y² < ½).
0,
otherwise.
Find
(a) P[(X,Y) € A], where A is the sector of the unit circle in the first quadrant
bounded by y = 0 and y = x

Expert Solution

Step 1

“Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved, then please specify the question number or post only that question.”

If f(x,y) is the joint probability density function then the marginal pdf of X is defined as

$g (x) = \int f (x, y) d y$

And the marginal pdf of Y is defined as

$h (y) = \int f (x, y) d x$

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