00:01
Hello students, in this problem, let's start by using the details balance equation for the stationary distribution of pi of a markov chain.
00:11
Equation is given pi i multiplied with p i, j is equal to p of j multiplied with i of j, i.
00:19
So this equation state that for any two state that is i to j in the markov chain.
00:27
So given condition that p of x, y is equal to c times p of x, z.
00:37
Well in this equation is in the state of y and z.
00:45
So therefore we can write that p of y, pi of y, y, x is equal to pi of x.
01:00
So these are the equation we get now replace p of x, y with values of so replace this value by c dot p x given z.
01:25
Because this is the given equation already defined this therefore the pi of y dot p of x, y is equal to pi of x dot c dot p of x, z.
01:44
Here we replace this term also pi of z dot p of z, x is equal to pi of x, x, z.
02:06
So this term get replaced from the above equation after that in both equation p of x, y and z of x p of z, x represent the probability of transition of the state x...