00:01
Hello students, if the system is in state i, so there are i white balls and 3 -i black balls.
00:06
So if the system is in state i, so there are i white balls and 3 -i black balls in the first one.
00:37
So now we need to compute the probabilities of our transitioning from state i to state j, where j is equal to 1, 2, 3.
00:46
So transition from state i to state i -1.
00:59
So this can happen if we draw a white ball from the first one, white ball from first one and a black ball from second one.
01:09
The probability of this happening is the probability of xn plus 1 equal to i minus 1 given xn equal to i, that is equal to i divided by 3 into i divided by 3 equal to i square by 9.
01:27
Next, we transition from state i to state i.
01:38
This is i minus 1 transition from state i to state i.
01:50
So this can happen in two ways.
01:58
Either we draw a white ball from both ends or we can draw a black ball from both ends.
02:11
So the probability of this happening is the probability of xn plus 1 equal to i given xn equal to i.
02:23
So i divided by 3 into 3 minus i by 3 plus 3 minus i by 3 into i by 3.
02:33
So it is equal to 6i minus 2i square by 9.
02:41
So now we transition from state i to state i plus 1.
02:53
So this can happen if we draw a black ball from first one and white ball from second one.
03:09
So here the probability of happening is the probability is probability of xn plus 1 equal to i plus 1 given xn equal to i, that is equal to 3 minus i divided by 3 into 3 minus i divided by 3.
03:23
That is equal to 3 minus i whole square by 9.
03:27
Next, we need to write the transition from state i to state j...