Assignment 2 Qu 4 (X2.4)

Hi,

There is something I am not quite getting here. I can follow through the answer to this, but am confused why we can't just use
p(ij) = mu(ij)/lambda(i)
to work out the transition matrix.

Using that I get:
P= 0 2/3 1/3
0 0 1
0 0 1

Then use (1/3, 1/3, 1/3)P to get the distribution at time 1.
Where am I missing the point?

Thanks...