Answer:
False. See te explanation an counter example below.
Step-by-step explanation:
For this case we need to find:
for all 
and for 
in the Markov Chain assumed. If we proof this then we have a Markov Chain
For example if we assume that 
then we have this:
Because we can only have if we have this:
, from definition given 
With 
we have that 
So based on these conditions 
would be 1 with probability 1/2 from the definition.
If we find a counter example when the probability is not satisfied we can proof that we don't have a Markov Chain.
Let's assume that 
for this case in order to satisfy the definition then 
But on this case that means 
and on this case the probability 
, so we have a counter example and we have that:
for all 
so then we can conclude that we don't have a Markov chain for this case.
The green mathematics tells about the impulse response of an in homogeneous linear differential operator.
According to the statement
we have to explain the green mathematics.
In mathematics, Actually there is a Green Function which was founded by a mathematician George Green.
In this function, a Green's function is the impulse response of an in homogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions.
The example of green function is the Green's function G is the solution of the equation LG = δ, where δ is Dirac's delta function; the solution of the initial-value problem Ly = f is the convolution (G ⁎ f), where G is the Green's function.
Actually in this function, it gives the relationship between the line integral of two dimensional vector over a closed path by a integral.
In this there is a green theorem, which relates a line integral around a simply closed plane curve C and a double integral over the region enclosed by C.
So, The green mathematics tells about the impulse response of an in homogeneous linear differential operator.
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