Question

What is the marginal distribution for right-handed people?
Short Medium Tall Total
Left-handed 4 6 2 12
Right-handed 24 20 19 63
Total 28 26 21 75

Answer 1

To find the marginal distribution for right-handed people, we want to summarize the values in the right-handed row of the table. The marginal distribution will show the total counts for each height category (Short, Medium, Tall) specifically for right-handed individuals.

From the given data for right-handed individuals:

- Short: 24
- Medium: 20
- Tall: 19

Now we can calculate the marginal distribution for right-handed people:

- Total for Short: 24
- Total for Medium: 20
- Total for Tall: 19
- Grand Total (Right-handed) = 63

Now we can express this as a probability:

- Marginal Probability for Short (Right-handed) = \( \frac{24}{63} \approx 0.38 \)
- Marginal Probability for Medium (Right-handed) = \( \frac{20}{63} \approx 0.32 \)
- Marginal Probability for Tall (Right-handed) = \( \frac{19}{63} \approx 0.30 \)

Thus, the marginal distribution for right-handed people is as follows:

\[
\begin{array}{|c|c|}
\hline
\text{Height} & \text{Right-handed Count} \\
\hline
\text{Short} & 24 \\
\text{Medium} & 20 \\
\text{Tall} & 19 \\
\hline
\text{Total} & 63 \\
\hline
\end{array}
\]

And in probability terms:

\[
\begin{array}{|c|c|}
\hline
\text{Height} & \text{Right-handed Probability} \\
\hline
\text{Short} & \frac{24}{63} \approx 0.38 \\
\text{Medium} & \frac{20}{63} \approx 0.32 \\
\text{Tall} & \frac{19}{63} \approx 0.30 \\
\hline
\end{array}
\]