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- 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.find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyzLinear DE of Order 1
- The number of defects on the front side (X) of a wooden panel and the number of defectsa 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. Determine the value of c.Minimize ƒ(x, y, z) = xy + yz subject x2 + y2 - 2 = 0 and x2 + z2 - 2 = 0.Consider a linear system: x`= ux + y, y`= -x + y, where u is a real constant. When is (0,0) an unstable saddle point? 2 when is (0,0) an unstable spiral point?
- Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).A container made of steel, which has a coefficient of linear expansion 11 ✕ 10−6 (°C)−1, has a volume of 46.0 gallons. The container is filled to the top with gasoline, which has a coefficient of volume expansion of 9.6 ✕ 10−4 (°C)−1, when the temperature is 10.0°C. If the temperature rises to 25.0°C, how much gasoline (in gal) will spill over the edge of the container? galLinear Homogeneous DE with Constant Coefficients