The correct answer is C. both using variables & information.
The full joint probability distribution is a table that shows the probability of each possible combination of outcomes for a set of variables. The entries in the table are calculated by multiplying the probabilities of the individual outcomes.
For example, if we have two variables, X and Y, with possible outcomes x1, x2, x3, and y1, y2, and y3, the full joint probability distribution would be:
P(X=x1, Y=y1) = P(X=x1) * P(Y=y1)
P(X=x1, Y=y2) = P(X=x1) * P(Y=y2)
P(X=x1, Y=y3) = P(X=x1) * P(Y=y3)
P(X=x2, Y=y1) = P(X=x2) * P(Y=y1)
P(X=x2, Y=y2) = P(X=x2) * P(Y=y2)
P(X=x2, Y=y3) = P(X=x2) * P(Y=y3)
P(X=x3, Y=y1) = P(X=x3) * P(Y=y1)
P(X=x3, Y=y2) = P(X=x3) * P(Y=y2)
P(X=x3, Y=y3) = P(X=x3) * P(Y=y3)
The probabilities of the individual outcomes can be calculated using a variety of methods, such as historical data, expert judgment, or simulation.
Once the full joint probability distribution is calculated, it can be used to answer a variety of questions about the relationship between the variables. For example, we can use it to calculate the probability of X=x1 and Y=y2, or the probability of X=x1 or Y=y2.