total 4 points suppose you have iid pairs of sample x1 y1 x2 y2xn yn y

Question

. (Total 4 points) Suppose you have iid pairs of sample (X1, Y1), (X2, Y2),..,(Xn, Yn). You wish to estimate a function M (t1, t2) defined by M\left(t_{1}, t_{2}\right)=E\left(e^{t_{1} X+t_{2}

Y}\right) where e is the natural number. Note that M(t1, t2) is a bivariate function of ti and t2 after taking the expectation. Provide a consistent estimator of M(t1, t2) and show the consistency.