If I have a discrete bivariate distribution with a probability mass function defined as
$$p(x, y) = \frac{x+y}{21}$$
for $x = 1, 2, 3$ and $y = 1,2$,
is then $P(X = Y)$ found by taking the following sum;
$$P(X = Y) = \sum_{\lbrace x,y |x = y \rbrace}p(x,y)?$$
I found the answer to be $P(X = Y) = \frac{2}{7}.$ Thanks.