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(0.2) (0.1) (1.1) (-2,0) (-1,0) (0.0) (1.0) (2.0) I (-1.-1) [(0.-1) (1.-1) (0.-2) Figure 5.4: Grid for example 5.4 Example 5.4 Consider the set of points in the grid shown in Figure 5.4. These are the points in set G defined as G - {(r. y) r. y € Z. + y < 2}. Suppose that we pick a point (X.Y) from this grid completely at random. Thus, each point has a probability of of being chosen. a. Find the joint and marginal PMFS of X and Y. b. Find the conditional PMF of X given Y = 1. C. Are X and Y independent?

(0.2) (0.1) (1.1) (-2,0) (-1,0) (0.0) (1.0) (2.0) I (-1.-1) [(0.-1) (1.-1) (0.-2) Figure 5.4: Grid for example 5.4 Example 5.4 Consider the set of points in the grid shown in Figure 5.4. These are the points in set G defined as G - {(r. y) r. y € Z. + y < 2}. Suppose that we pick a point (X.Y) from this grid completely at random. Thus, each point has a probability of of being chosen. a. Find the joint and marginal PMFS of X and Y. b. Find the conditional PMF of X given Y = 1. C. Are X and Y independent?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 9E
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(0.2) (-1.1) (0.1) (1.1) (-2,0) (-1,0) (0.0) (1.0) (2,0) I (-1.-1) |(0.-1) (1.-1) (0.-2) Figure 5.4: Grid for example 5.4 Example 5.4 Consider the set of points in the grid shown in Figure 5.4. These are the points in set G defined as G - {(x. y)|r. y€ Z. x + y < 2}. Suppose that we pick a point (X,Y) from this grid completely at random. Thus, each point has a probability of - of being chosen. a. Find the joint and marginal PMFS of X and Y. b. Find the conditional PMF of X given Y = 1. C. Are X and Y independent?
Transcribed Image Text:(0.2) (-1.1) (0.1) (1.1) (-2,0) (-1,0) (0.0) (1.0) (2,0) I (-1.-1) |(0.-1) (1.-1) (0.-2) Figure 5.4: Grid for example 5.4 Example 5.4 Consider the set of points in the grid shown in Figure 5.4. These are the points in set G defined as G - {(x. y)|r. y€ Z. x + y < 2}. Suppose that we pick a point (X,Y) from this grid completely at random. Thus, each point has a probability of - of being chosen. a. Find the joint and marginal PMFS of X and Y. b. Find the conditional PMF of X given Y = 1. C. Are X and Y independent?
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