Can the vector be a probability vector? If not, why? 4 1 5 5 Yes, the components sum to 1. Yes, the vector is a 1 x 2. No, the components do not sum to 1. No, the vector is a 2 x 1.
Can the vector be a probability vector? If not, why? 4 1 5 5 Yes, the components sum to 1. Yes, the vector is a 1 x 2. No, the components do not sum to 1. No, the vector is a 2 x 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Question:** Can the vector be a probability vector? If not, why?
**Vector:**
\[
\begin{bmatrix}
\frac{4}{5} \\
\frac{1}{5}
\end{bmatrix}
\]
**Options:**
- ○ Yes, the components sum to 1.
- ○ Yes, the vector is a 1 x 2.
- ○ No, the components do not sum to 1.
- ○ No, the vector is a 2 x 1.
**Explanation:**
A probability vector is a vector of non-negative numbers that sum up to 1. In this case, the vector is:
\[
\begin{bmatrix}
\frac{4}{5} \\
\frac{1}{5}
\end{bmatrix}
\]
The components are \(\frac{4}{5}\) and \(\frac{1}{5}\).
- **Sum of components:** \(\frac{4}{5} + \frac{1}{5} = \frac{5}{5} = 1\)
Therefore, the components do indeed sum to 1. The vector is a 2 x 1 column vector, meaning it has two rows and one column. The correct option is:
- ○ Yes, the components sum to 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8533e211-c3b0-4c2c-a0a5-c3ff9e21dbc2%2F85ff6aa9-1e09-4ca3-8ced-c0bf57e585ef%2Fxzflh8l_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:** Can the vector be a probability vector? If not, why?
**Vector:**
\[
\begin{bmatrix}
\frac{4}{5} \\
\frac{1}{5}
\end{bmatrix}
\]
**Options:**
- ○ Yes, the components sum to 1.
- ○ Yes, the vector is a 1 x 2.
- ○ No, the components do not sum to 1.
- ○ No, the vector is a 2 x 1.
**Explanation:**
A probability vector is a vector of non-negative numbers that sum up to 1. In this case, the vector is:
\[
\begin{bmatrix}
\frac{4}{5} \\
\frac{1}{5}
\end{bmatrix}
\]
The components are \(\frac{4}{5}\) and \(\frac{1}{5}\).
- **Sum of components:** \(\frac{4}{5} + \frac{1}{5} = \frac{5}{5} = 1\)
Therefore, the components do indeed sum to 1. The vector is a 2 x 1 column vector, meaning it has two rows and one column. The correct option is:
- ○ Yes, the components sum to 1.
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