Please solve b, d, and f parts.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Please solve b, d, and f parts.
![Two safety inspectors inspect a new building and assign it a “safety score” of 1, 2, 3, or 4. Suppose that the random variable \(X\) is the score assigned by the first inspector and the random variable \(Y\) is the score assigned by the second inspector. They have a joint probability mass function given below:
\[
\begin{array}{c|c|c|c|c|}
Y \backslash X & 1 & 2 & 3 & 4 \\
\hline
1 & 0.09 & 0.03 & 0.01 & 0.01 \\
\hline
2 & 0.02 & 0.15 & 0.03 & 0.01 \\
\hline
3 & 0.01 & 0.01 & 0.24 & 0.04 \\
\hline
4 & 0.00 & 0.01 & 0.02 & 0.32 \\
\hline
\end{array}
\]
(a) **What is the probability that both inspectors assign the same safety score?**
(b) **What is the probability that the second inspector assigns a higher safety score than the first inspector?**
(c) **What are the marginal probability mass function, expectation, and variance of the score assigned by the first inspector?**
(d) **What are the marginal probability mass function, expectation, and variance of the score assigned by the second inspector?**
(e) **Are the scores assigned by the two inspectors independent of each other?**
(f) **What are the covariance of the scores assigned by the two inspectors?**
**Explanation of the Table:**
- The table shows the joint probability mass function of the scores assigned by two inspectors.
- \(X\) represents the scores given by the first inspector and \(Y\) represents scores by the second inspector.
- Each cell in the table provides the probability of the specified pair of scores being assigned: \(P(X=x, Y=y)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5795113b-12be-4a88-b99a-1067a434ff37%2F2342ca4c-6587-44f3-9c9c-0112853ec720%2Fcy6f2cp_processed.png&w=3840&q=75)
Transcribed Image Text:Two safety inspectors inspect a new building and assign it a “safety score” of 1, 2, 3, or 4. Suppose that the random variable \(X\) is the score assigned by the first inspector and the random variable \(Y\) is the score assigned by the second inspector. They have a joint probability mass function given below:
\[
\begin{array}{c|c|c|c|c|}
Y \backslash X & 1 & 2 & 3 & 4 \\
\hline
1 & 0.09 & 0.03 & 0.01 & 0.01 \\
\hline
2 & 0.02 & 0.15 & 0.03 & 0.01 \\
\hline
3 & 0.01 & 0.01 & 0.24 & 0.04 \\
\hline
4 & 0.00 & 0.01 & 0.02 & 0.32 \\
\hline
\end{array}
\]
(a) **What is the probability that both inspectors assign the same safety score?**
(b) **What is the probability that the second inspector assigns a higher safety score than the first inspector?**
(c) **What are the marginal probability mass function, expectation, and variance of the score assigned by the first inspector?**
(d) **What are the marginal probability mass function, expectation, and variance of the score assigned by the second inspector?**
(e) **Are the scores assigned by the two inspectors independent of each other?**
(f) **What are the covariance of the scores assigned by the two inspectors?**
**Explanation of the Table:**
- The table shows the joint probability mass function of the scores assigned by two inspectors.
- \(X\) represents the scores given by the first inspector and \(Y\) represents scores by the second inspector.
- Each cell in the table provides the probability of the specified pair of scores being assigned: \(P(X=x, Y=y)\).
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