Neural Machine Translation A Review Of Methods Resources And Tools Sciencedirect STAT 400 Joint Probability Distributions Fall 17 1 Let X and Y have the joint pdf f X, Y (x, y) = C x 2 y 3, 0 < x < 1, 0 < y < x, zero elsewhere a) What must the value of C be so that f X, Y (x, y) is a valid joint pdf?b) Find P (X Y < 1)c) Let 0 < a < 1 Find P (Y < a X) d) Let a > 1 Find P (Y < a X)e) Let 0 < a < 1 Find P (X Y < a)Equation (ode) P(x,y)dxQ(x,y)dy = 0 If ∂P ∂y = ∂Q ∂x then the ode is said to be exact This means that a function u(x,y) exists such that du = ∂u ∂x dx ∂u ∂y dy = P dxQdy = 0 One solves ∂u ∂x = P and ∂u ∂y = Q to find u(x,y) Then du = 0 gives u(x,y) = C, where C is a constant |Pxy C[uC o»ê