Test2solns - University of Toronto at Mississauga STA457H5F Fall 2009 Term Test#2 Aids Allowed Any calculator without text keyboard 1(14 marks

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pg. 1 Aids Allowed: Any calculator without text keyboard 1. (14 marks) Consider the following difference equation: y t – 1.5 y t-1 – y t-2 = 1 where y 0 = 1 and y 1 = 0 a. Find the roots of the characteristic equation. Soln 2 and –½ b. What is the homogeneous solution, y t h ? Soln y t h = A 1 (2) t + A 2 (-½) t c. Is this process stable? Explain your answer Soln No, since one root is 2 which is outside the unit circle. d. Does this process oscillate? Explain your answer Soln In the short run there are small oscillations, but none in the long run e. Find a particular solution, y t p Soln y t p = -2/3 University of Toronto at Mississauga STA457H5F - Fall 2009 Term Test #2
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pg. 2 f. What is the general solution? Soln y t = A 1 (2) t + A 2 (-½) t - 2/3 g. Use the initial conditions to find the specific solution. Soln y t = (9/15)(2) t + (16/15)(-½) t - 2/3 2. (8 marks) Consider the following difference equation: y t – 0.4 y t-1 + 0.13 y t-2 = 1 a. This difference equation could be expressed as A(L)y
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Test2solns - University of Toronto at Mississauga STA457H5F Fall 2009 Term Test#2 Aids Allowed Any calculator without text keyboard 1(14 marks

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