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Erik Strand
pit
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2593c9cb
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2593c9cb
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Feb 16, 2019
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Erik Strand
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@@ -148,14 +148,15 @@ of that current?
## 3.4
This problem is much harder than the others. Consider a stochastic process $$x(t)$$ that randomly
switches between x = 0 and x = 1. Let $$
\a
lpha
\m
athrm{d}t$$ be the probability that it makes a transition from 0 to 1
during the interval $$
\m
athrm{d}t$$ if it starts in x = 0, and let $$
\b
eta
\m
athrm{d}t$$ be the probability that it makes a
transition from 1 to 0 during $$
\m
athrm{d}t$$ if it starts in x = 1.
switches between x = 0 and x = 1. Let $$
\a
lpha
\m
athrm{d}t$$ be the probability that it makes a
transition from 0 to 1 during the interval $$
\m
athrm{d}t$$ if it starts in x = 0, and let $$
\b
eta
\m
athrm{d}t$$ be the probability that it makes a transition from 1 to 0 during $$
\m
athrm{d}t$$ if it
starts in x = 1.
### (a)
Write a matrix differential equation for the change in time of the probability $$p_0(t)$$ to be in
the 0
state and the probability $$p_1(t)$$ to be in the 1 state.
Write a matrix differential equation for the change in time of the probability $$p_0(t)$$ to be in
the 0
state and the probability $$p_1(t)$$ to be in the 1 state.
### (b)
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