1. Marginal and Conditional Probabilities Consider the following joint distribution. Xo X₁ X₂ P(X0, X1, X₂) 0 0 0 0.100 0 1 0.200 1 0.000 1 0.150 0 0 0 1 1 0 0 0 1 0 1 0.150 0.120 1 1 Calculate the following probabilities 1 0 1 1 0.100 0.180 (a) P(Xo = 1, X₁ = 0, X₂ = 1) (b) P(Xo = 0, X₁ = 1) (c) P(Xo = 1) (d) P(X₁ = 0 | Xo = 1) (e) P(X₁ = 0, X₂ = 1 | Xo = 1) (f) P(X₁=0 | Xo = 1, X₂ = 1) 2. Independence In the joint distribution from the previous problem, is Xo independent of X₁? Justify your answer.
1. Marginal and Conditional Probabilities Consider the following joint distribution. Xo X₁ X₂ P(X0, X1, X₂) 0 0 0 0.100 0 1 0.200 1 0.000 1 0.150 0 0 0 1 1 0 0 0 1 0 1 0.150 0.120 1 1 Calculate the following probabilities 1 0 1 1 0.100 0.180 (a) P(Xo = 1, X₁ = 0, X₂ = 1) (b) P(Xo = 0, X₁ = 1) (c) P(Xo = 1) (d) P(X₁ = 0 | Xo = 1) (e) P(X₁ = 0, X₂ = 1 | Xo = 1) (f) P(X₁=0 | Xo = 1, X₂ = 1) 2. Independence In the joint distribution from the previous problem, is Xo independent of X₁? Justify your answer.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Question 1 part C D and E F please.
Transcribed Image Text:1. Marginal and Conditional Probabilities
Consider the following joint distribution.
Xo X₁ X₂ P(X0, X1, X2)
0
0
0
0.100
0
1
0.200
0.000
0.150
0.150
0.120
0
0
1
1
1
0
1 0
1
1
lolo
0
0
0
1
1
0
1 1
0.100
0.180
1
Calculate the following probabilities
(a) P(Xo = 1, X₁ = 0, X₂ = 1)
(b) P(Xo = 0, X₁ = 1)
(c) P(Xo = 1)
(d) P(X₁ = 0 | Xo = 1)
(e) P(X₁ = 0, X₂ = 1 | Xo = 1)
(f) P(X₁ = 0 | Xo = 1, X₂ = 1)
2. Independence In the joint distribution from the previous problem, is Xo independent of X₁? Justify
your answer.
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