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Let X and Y have a uniform distribution on the set of

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 9E Chapter 4.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 9E

Let \(X\) and \(Y\) have a uniform distribution on the set of points with integer coordinates in \(S=\{(x, y): 0 \leq x \leq\) \(7, x \leq y \leq x+2\}\). That is, \(f(x, y)=1 / 24,(x, y) \in S\), and both \(x\) and \(y\) are integers. Find

(a) \(f_{X}(x)\).

(b) \(h(y \mid x)\).

(c) \(E(Y \mid x)\).

(d) \(\sigma_{Y \mid x}^{2}\).

(e) \(f_{Y}(y)\).

Equation Transcription:

.

.

.


Text Transcription:

X  

Y  

S={(x,y):0< or = x < or = 7,x< or = y< or = x+2}  

f(x,y)=1/24,(x,y) in S  

x

y  

f_X(x)  

h(y∣x) .

E(Y∣x) .

sigma_Y∣x^2

f_Y (y)

Step-by-Step Solution:

Step 1 of 6 :

Given that X and Y are uniformly distributed with f(x,y)=;0xyx+2 on the set of points on the integer coordinate S={(x,y),0xyx+2}.The given uniform distribution is a discrete uniform distribution, since the set S has only a finite number of outcomes with equal probability.


Step 2 of 6

Chapter 4.3, Problem 9E is Solved
Step 3 of 6

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Let X and Y have a uniform distribution on the set of