Answer:
P(X = x, Y = y) = f(x, y)
Step-by-step explanation:
Let X be a discrete random variable, and suppose that the possible values that it can assume are given by x1, x2, x3, . . . , arranged in some order. Suppose also that these values are assumed with probabilities given by
P(X = xk) = f(xk) k = 1, 2, . . . (1)
It is convenient to introduce the probability function, also referred to as probability distribution, given by
P(X = x) = f(x)
If X and Y are two discrete random variables, we define the joint probability function
of X and Y by
P(X = x, Y = y) = f(x, y)
where f(x, y) ≥ 0
.
,
