Question 1 part A B and C please. # Marginal and Conditional ProbabilitiesConsider the following joint distribution.| $X_0$ | $X_1$ | $X_2$ | $P(X_0, X_1, X_2)$ ||---------|---------|---------|-----------------------|| 0 | 0 | 0 | 0.100 || 0 | 0 | 1 | 0.200 || 0 | 1 | 0 | 0.000 || 0 | 1 | 1 | 0.150 || 1 | 0 | 0 | 0.150 || 1 | 0 | 1 | 0.120 || 1 | 1 | 0 | 0.100 || 1 | 1 | 1 | 0.180 |Calculate the following probabilities:(a) $ P(X_0 = 1, X_1 = 0, X_2 = 1) $(b) $ P(X_0 = 0, X_1 = 1) $(c) $ P(X_0 = 1) $(d) $ P(X_1 = 0 \mid X_0 = 1) $(e) $ P(X_1 = 0, X_2 = 1 \mid X_0 = 1) $(f) $ P(X_1 = 0 \mid X_0 = 1, X_2 = 1) $# IndependenceIn the joint distribution from the previous problem, is $X_0$ independent of $X_1$? Justify your answer.

a) PX0=1,X1=0,X2=1=0.120, from the given table

Answered: 1. Marginal and Conditional…

1. Marginal and Conditional Probabilities Consider the following joint distribution. Xo|X1|X₂|| P(X0, X1, X₂) 000 0.100 001 0.200 0 1 0 1 1 0 0 1 0 0.000 0.150 0.150 0 120

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

Question 1 part A B and C please.

# Marginal and Conditional Probabilities

Consider the following joint distribution.

| $X_0$ | $X_1$ | $X_2$ | $P(X_0, X_1, X_2)$ |
|---------|---------|---------|-----------------------|
| 0 | 0 | 0 | 0.100 |
| 0 | 0 | 1 | 0.200 |
| 0 | 1 | 0 | 0.000 |
| 0 | 1 | 1 | 0.150 |
| 1 | 0 | 0 | 0.150 |
| 1 | 0 | 1 | 0.120 |
| 1 | 1 | 0 | 0.100 |
| 1 | 1 | 1 | 0.180 |

Calculate the following probabilities:

(a) $ P(X_0 = 1, X_1 = 0, X_2 = 1) $

(b) $ P(X_0 = 0, X_1 = 1) $

(c) $ P(X_0 = 1) $

(d) $ P(X_1 = 0 \mid X_0 = 1) $

(e) $ P(X_1 = 0, X_2 = 1 \mid X_0 = 1) $

(f) $ P(X_1 = 0 \mid X_0 = 1, X_2 = 1) $

# Independence

In the joint distribution from the previous problem, is $X_0$ independent of $X_1$? Justify your answer.

Expert Solution

Step 1

$P (X_{0} = 1, X_{1} = 0, X_{2} = 1) = 0.120, f r o m t h e g i v e n t a b l e$

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