Final answer:
To find the marginal distribution of X and Y, we need the joint probability distribution table to sum the probabilities across rows for X and columns for Y. Unfortunately, the actual joint distribution table is missing, and thus the correct marginal distributions cannot be determined from the provided options without it.
Step-by-step explanation:
To find the marginal distribution of two random variables X and Y based on a joint probability distribution, we sum the probabilities across the rows and columns respectively. The marginal distribution of X is the sum of probabilities across the rows for each X value, whereas the marginal distribution of Y is the sum of probabilities across the columns for each Y value. This tells us about the probability distribution of a single variable without regard to the other variable.
The given options seem to be missing the actual joint probability distribution table that provides the frequencies or probabilities for the combinations of X and Y. However, if we had such a table at our disposal, we would proceed as follows:
- For each value X might take on, sum the joint probabilities across the corresponding row. This will yield the marginal distribution of X.
- For each value Y might take on, sum the joint probabilities across the corresponding column. This will yield the marginal distribution of Y.
Keep in mind, the values in the marginal distributions themselves must also add up to 1, as they represent the total probability distribution for the variable in question.
Without a specific joint probability distribution given, we cannot definitively select from the provided options (A, B, C, or D). It is crucial to have the joint probability distribution table in order to perform this calculation correctly.