We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters α_1,β_1 and α_2,β_2 in finding the nth moment of the variable x~cy~d (c≥0,d≥0) where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called g_n(c,d) defined g_n(c,d)=E(X~cY~d+γ)~n, the nth moment of expected value of the t distribution of the cth power of X and dth power of Y about the constant γ. These moments are obtained by the use of bi-variate moment generating functions, when they exist. The proposed g_n(c,d) is illustrated with some continuous bi-variate distributions and is shown to be easy to use even when the powers of the random variables being considered are non-negative real numbers that need not be integers. The results obtained using g_n(c,d) are the same as results obtained using other methods such as moment generating functions when they exist.
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