Let (x1, x2, x3, x4) be multinomial(n, 4, 1/6, 1/3, 1/8, 3/8). derive the joint mass function of the pair (x3, x4). you should be able to do this with almost no computation.

The random variables in this case are discrete since they have a Multinomial distribution.

The probability mass function for a discrete random variable X is given by:

Where are are possible values of X.

The joint probability mass function of two discrete random variables X and Y is defined as

P(x,y) =P(X=x,Y=y).

It follows that, The joint probability mass function of is :