2 -1 -2 -3 -4 2 Scenario 1 3 2 1 ° -1 Scenario 2 Scenario 3 5 -5 -4 -3 -2 -1 1 3 -5 -4 -3 -2 -1 01 Scenario 4 4 3 1 0 -1 -2 -3 -4 Scenario 5 4 3 2 1 ° -1 -2 -3 -5 3 -5 -4 -3 -2 -1 1 2 3 4 Scenario 6 4 3 2 1 0 -1 -2 -3 -5 -5 -5 -5 -4 -3 -2 -1 1 3 5 -5 -3 -1 1 3 -5 -1 0 1 2 3 4 5

2 -1 -2 -3 -4 2 Scenario 1 3 2 1 ° -1 Scenario 2 Scenario 3 5 -5 -4 -3 -2 -1 1 3 -5 -4 -3 -2 -1 01 Scenario 4 4 3 1 0 -1 -2 -3 -4 Scenario 5 4 3 2 1 ° -1 -2 -3 -5 3 -5 -4 -3 -2 -1 1 2 3 4 Scenario 6 4 3 2 1 0 -1 -2 -3 -5 -5 -5 -5 -4 -3 -2 -1 1 3 5 -5 -3 -1 1 3 -5 -1 0 1 2 3 4 5

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

We have provided several scenarios describing pairs of (continuous) random variables via contour plots, scatter plots, and equations. For each of the following parts, list the scenarios that satisfy the specified criteria. For the equations, this will require some quick calculations, but for the contour and scatter plots you should be able to reason visually without calculations.

(a) E[X] noticeably more than 0

(b) E[Y ] noticeably less than 0

(d) Cov[X, Y ] noticeably more than 0

(e) absolute val (ρX,Y) close to 1

2
-1
-2
-3
-4
2
Scenario 1
3
2
1
°
-1
Scenario 2
Scenario 3
5
-5
-4
-3
-2
-1
1
3
-5
-4
-3
-2
-1 01
Scenario 4
4
3
1
0
-1
-2
-3
-4
Scenario 5
4
3
2
1
°
-1
-2
-3
-5
3
-5
-4
-3
-2
-1
1
2 3 4
Scenario 6
4
3
2
1
0
-1
-2
-3
-5
-5
-5
-5
-4
-3
-2
-1
1
3
5
-5
-3
-1
1
3
-5
-1
0
1
2
3
4
5

Definition Definition Representation of the direction and degree of correlation in graphical form. The grouping of points that are plotted makes it a scatter diagram. A line can be drawn showing the relationship based on the direction of points and their distance from each other.

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