- #1
Razberryz
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Homework Statement
In any given year a person may or may not get the flu. Past records show that if a person has the flu one year then (due to a build up of antibodies) there is a 85% chance that they will not get the flu in the following year. If they don't have a flu in a given year then there is a 25% chance that they will get the flu the following year.
(a) If a person has the flu one year, what is the probability that they will also have the flu 2 years later?
(b) In the long run, what proportion of years does a person not have the flu?
Homework Equations
x(t) = Ptx(0)
The Attempt at a Solution
\begin{bmatrix}5/17 & -1 \\ 1 & 1 \end{bmatrix}\begin{bmatrix}1^t & 0 \\ 0 & -0.1^t \end{bmatrix}\begin{bmatrix}5/17 & 0.1 \\ 1 & -0.1 \end{bmatrix}\begin{bmatrix}x_1(0) \\ x_2(0) \end{bmatrix}
first matrix is the eigenvectors
second in the diagonal
third is the multiplication of the first and second
4th is the original population I guess, which I don't know
According to an example from my notes, I think I'm supposed to multiply all these 4 matrices together which I did, and I got
(\begin{bmatrix}25/289 & 1/34 \\ 5/17 & 0.1 \end{bmatrix})*(\begin{bmatrix}x_1(0) \\ x_2(0) \end{bmatrix})
I don't know where to go from here. Any help appreciated.