The distributions of X and of Y are described here. If X and Y are independent, determine the joint probability distribution of X and Y.

It should be noted that the p.f of X and Y when they are independent can be obtained by multiplying together their marginal probability function.

Step-by-step explanation:

Two discrete random variables X and Y are said to be statistically independent if and only if , for all possible values ( xi, yi) the joint probability function f(x,y) can be expressed as the product of two marginal functions. That is X and y are independent if

f(x,y) = P(x=xi  and Y =yi)

          =  P(x=xi) P(Y =yi)         for all i and j

            = g(x)h(y)

It should be noted that the p.f of X and Y when they are independent can be obtained by multiplying together their marginal probability function.

The values of marginal probabilities are often written in the margins of the joint table as there are rows and columns totals in the table. The probabilities in each marginal probability function add to 1.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^