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One of the well-known class of models that involve a simple difference equation are models of mean reversion. These models typically take the form
yt+1 - yt = -a(yt - μ)where 0 < a< 1
In the equation above μ is the mean of yt.
a) Provide the intuitive explanation for the above equation.
b) Show homogenous, particular and then general solution for the difference equation.
c) Setting t=0 show the solution to the mean-reversion model.
d) Analyze the dynamic path of this model.
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
Proof of Root Test Firstly note that we can suppose without loss of generality that the series will initiate at n = 1 as we've done for all our series test proofs. As well n
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Examples on Log rules: Example: Calculate (1/3)log 10 2. Solution: log b n√A = log b A 1/n = (1/n)log b A (1/3)log 10 2 = log 10 3 √2 = log 10 1.
1+1=
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a. Cassie has seven skirts, five blouses, and ten pairs of shoes. How many possible outfits can she wear? b. Cassie decides that four of her skirts should not be worn to school.
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