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- considering the nonhomogenous 2ndorder ode y'' + 4y = 10sin(9pi x t)II) Classify the PDE (1 + x)²Uxx - 4xUxy + Uyy = x.A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=3,Y=4).
- Change Ax = b to x = (I -A)x + b. What are Sand T for this splitting? What matrix s-1y controls the convergence of Xk+l = (I -A)xk + b?Determine if the following is a fundemental set of solutions to y'' -6y' + 25 = 0 Given that y1=e3xcos(4x) and y2= e3xsin(4x)The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent.