Compute the mean of a Poisson distribution by hand. Show intermediate steps.
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Compute the mean of a Poisson distribution by hand. Show intermediate steps.
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- 3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0Given: Time, t (s) 0 2 4 6 8 10 Position, x (m) 0 0 0.7 1.8 3.4 5.1 6.3 Using Centered-Finite Difference Method, find: find the velocities 12 14 16 7.3 8.0 8.4Q-2) Find the solution for the LPP below by using the graphical method? Min Z=4x1+3x2 S.to: x1+2x2<6 2x1+x2<8 x127 x1,x2 ≥ 0 Is there an optimal solution and why if not can you extract it?
- 3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0Solve step by step2. Solve the following ODE in space using finite difference method based on central differences with error O(h). Use a five node grid. 4u" - 25u0 (0)=0 (1)=2 Solve analytically and compare the solution values at the nodes.
- (3) For the given boundary value problem, the exact solution is given as = 3x - 7y. (a) Based on the exact solution, find the values on all sides, (b) discretize the domain into 16 elements and 15 evenly spaced nodes. Run poisson.m and check if the finite element approximation and exact solution matches, (c) plot the D values from step (b) using topo.m. y Side 3 Side 1 8.0 (4) The temperature distribution in a flat slab needs to be studied under the conditions shown i the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I all cases assume the upper and lower boundaries are insulated. Assume that the units of length energy, and temperature for the values shown are consistent with a unit value for the coefficier of thermal conductivity. Boundary Temperatures 6 Case A C D. D. 00 LEGION Side 4 z epis3.1-6 DI 3.1-6. Use the graphical method to solve the problem: Maximize Z = 10x + 20x2, subject to -X + 2x, s 15 X1 + x2 < 12, 5x, + 3x s 45 and X 0, x2 2 0. 3.1-11 (a) and (b) only For (a), please specify: (1) Decision variables; (2) Objective function; (3) Constraints. MacBook Pro1. The following transportation problem of cost matrix is: Destination Supply A 7. 10 6. 80 15 Demand 75 20 50 Sources Requirement: Is it what type of transportation problem? Discuss the other types of it. The penalty costs for not satisfying demand at the warehouses D, E, and F are TK. 5, 3, and 2 per unk respectively. Determine minimum transportation cost by using Lest Cost Method (LCM)