https://file.aiquickdraw.com/mathbot/file/17288665516778a83jn0h.jpg

Let's break down the steps to solve this:

### Part (a): Marginal Distribution
- You need to sum the values across the rows and columns to fill in the marginal distribution for both \(y_1\) and \(y_2\), as well as the totals for \(x_1, x_2, x_3\).

- For \(y_1\):
  \[
  50 + 15 + 30 = 95
  \]

- For \(y_2\):
  \[
  30 + 25 + 50 = 105
  \]

- For \(x_1\):
  \[
  50 + 30 = 80
  \]

- For \(x_2\):
  \[
  15 + 25 = 40
  \]

- For \(x_3\):
  \[
  30 + 50 = 80
  \]

Thus, the marginal distribution table looks like this:

|   | \(x_1\) | \(x_2\) | \(x_3\) | Total (y) |
|---|--------|--------|--------|-----------|
| \(y_1\) | 50    | 15    | 30    | **95**    |
| \(y_2\) | 30    | 25    | 50    | **105**   |
| Total (x) | **80**  | **40**  | **80**  | **160**    |

### Part (b): Relative Frequency Marginal Distribution
To get the relative frequencies, divide each cell by the total sum, which is 160:

- \(y_1\):
  \[
  \frac{95}{160} = 0.59375 \approx 0.594
  \]

- \(y_2\):
  \[
  \frac{105}{160} = 0.65625 \approx 0.656
  \]

For \(x_1\):
\[
\frac 124/160 calculating

Consider the dataset provided and calculate the marginal distribution, relative frequency marginal distribution, and conditional distribution. Then, select the correct bar graph representing the conditional distribution.

Learn how to calculate marginal distributions, relative frequency distributions, and conditional distributions from a given dataset. This problem involves applying basic probability concepts and interpreting the results graphically.

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