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- Solve the following equation using the Gaussian Elimination MethodMake sure to show the correct work and solution: Suppose P(X = 0, Y = 0) = 1/3, P(X = 0, Y = 3) = 1/3, and P(X = 6, Y = 3) = 1/3. Find Cov(X, Y ) and the correlation ρ of X and Y .Solve a real-life working example of Newton's forward interpolation method, take random 5 values for x and y.
- Use Variation of Parameters to solve the DE y′′ − 4y = e2x2. Give the condition which ensure that |ez| < 1 where z in C.What is the trial particular solution for g(x) = (x2 - 1) sin2x a.) yp = (Ax2 + B) sin2x b.) yp = (Ax2 - B) sin2x c.) yp = (Ax2 - B) sin2x + (Cx2 - E) cos2x d.) yp = (Ax2 + B) sin2x + (Cx2 + E) cos2x e.) yp = (Ax2 + Bx + C) sin2x + (Ex2 + Fx + G) cos2x f.) yp = (Ax2 + Bx - C) sin2x g.) yp = (Ax2 + Bx + C) sin2x h.) yp = (Ax2 + Bx - C) sin2x + (Ex2 + Fx - G) cos2x
