Q.From the bivariate frequency table constructed in Worked Example 1, write down

The marginal distribution of a variable is read straight from the totals of the two-way table — row totals for $x$, column totals for $y$.

Marginal of $x$: $x=1 \to 4$, $x=2 \to 5$, $x=3 \to 3$.

Marginal of $y$: $y=1 \to 4$, $y=2 \to 5$, $y=3 \to 3$.

Step 1 — Recall the table (from Worked Example 1).

Step 2 — Part (i): marginal distribution of $x$. Ignoring $y$, add across each row (these are the row totals):

Step 3 — Part (ii): marginal distribution of $y$. Ignoring $x$, add down each column (these are the column totals):

Independent check. Both marginal distributions add to $12 = N$, and each is just the appropriate set of totals lifted directly from the margins of the two-way table — no arithmetic beyond the totals already computed in Worked Example 1 is needed.

Confusing the marginal distribution of $x$ (the row totals) with the marginal distribution of $y$ (the column totals) is the usual mix-up — remember the marginal of a variable is found by summing over the other variable, so $x$'s marginal comes from adding along each $x$-row. That the two marginals happen to be numerically equal here ($4,5,3$ both ways) is a coincidence of this particular data, not a rule.