Final answer:
The question involves finding the joint moment generating function (MGF) for two random variables, which includes obtaining marginal MGFs by setting the corresponding time parameter to zero. This is a typical exercise in a college-level statistics course.
Step-by-step explanation:
The question relates to the field of probability and statistics, more specifically, to the concept of joint moment generating functions (MGFs) for random variables. We are given two random variables, X1 and X2, and asked to find their joint MGF. The joint MGF, Mx1,x2(t1,t2), is a function that gives us information about the moments of the joint distribution of X1 and X2.
To find the joint MGF, we typically would integrate the joint pdf of X1 and X2 multiplied by the exponential function et1x1+t2x2 over all possible values of x1 and x2. From the joint MGF, one can obtain marginal MGFs by setting t1 or t2 to zero in the joint MGF,.
The expressions Mx1,x2(t1=0,t2) and Mx1,x2(t1,t2=0) represent the marginal MGFs of X2 and X1 respectively since setting one variable's parameter to zero effectively integrates out that variable.