Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![The image contains a statistical exercise involving probability distributions for a random variable \( Y \). On the left, there's information about the probability distribution of \( Y \), and on the right, there's an incomplete table to be filled out for the transformed variable \(\frac{1}{5}Y\).
### Left Side:
#### Problem Description:
"Let the random variable \( Y \) have the probability distribution listed in the table below. Determine the probability distributions of the random variable \(\frac{1}{5}Y\)."
#### Probability Distribution of \( Y \):
| \( k \) | \( \Pr(Y = k) \) |
|---------|------------------|
| 5 | 0.2 |
| 10 | 0.3 |
| 15 | 0.2 |
| 20 | 0.2 |
| 25 | 0.1 |
### Right Side:
#### Task:
"Fill in the table for the probability distribution of the variable \(\frac{1}{5}Y\)."
#### Incomplete Table:
The table to be filled:
| \( k \) | \( \Pr\left(\frac{1}{5}Y = k\right) \) |
|---------|---------------------------------------|
| 1 | [ ] |
| 2 | [ ] |
| 3 | [ ] |
| 4 | [ ] |
| 5 | [ ] |
The task consists of using the given probability distribution of \( Y \) to calculate the corresponding probabilities for \(\frac{1}{5}Y\) and fill out the right-hand table.](https://content.bartleby.com/qna-images/question/a5aa36f0-fa96-44c9-9490-28bf7ea812b5/f78916a1-34a8-44a0-a035-3e7fd667607e/c6ekr_processed.jpeg)
Transcribed Image Text:The image contains a statistical exercise involving probability distributions for a random variable \( Y \). On the left, there's information about the probability distribution of \( Y \), and on the right, there's an incomplete table to be filled out for the transformed variable \(\frac{1}{5}Y\).
### Left Side:
#### Problem Description:
"Let the random variable \( Y \) have the probability distribution listed in the table below. Determine the probability distributions of the random variable \(\frac{1}{5}Y\)."
#### Probability Distribution of \( Y \):
| \( k \) | \( \Pr(Y = k) \) |
|---------|------------------|
| 5 | 0.2 |
| 10 | 0.3 |
| 15 | 0.2 |
| 20 | 0.2 |
| 25 | 0.1 |
### Right Side:
#### Task:
"Fill in the table for the probability distribution of the variable \(\frac{1}{5}Y\)."
#### Incomplete Table:
The table to be filled:
| \( k \) | \( \Pr\left(\frac{1}{5}Y = k\right) \) |
|---------|---------------------------------------|
| 1 | [ ] |
| 2 | [ ] |
| 3 | [ ] |
| 4 | [ ] |
| 5 | [ ] |
The task consists of using the given probability distribution of \( Y \) to calculate the corresponding probabilities for \(\frac{1}{5}Y\) and fill out the right-hand table.
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