1. ## Markov chain problem

The coat of a certain breed of cat can be either black, white or grey.
When a black-coated male is crossed with a white-coated female, the offspring kitten has a 50% chance of having a black coat, and a 50% chance of having a white coat.

When a white-coated male is crossed with a white-coated female, the offspring kitten has a 20% chance of having a black coat, a 60% chance of having a white coat and a 20% chance of haing a grey coat.

When a grey-coated male is crossed with a white-coated female, the offspring kitten has a 10% chance of having a black coat, a 45% chance of having a white coat and a 45% chance of having a grey coat.

(a) Assume that each successive generation of cats is produced by crossing all cats with a white-coated female. Write down the transition matrix for this Markov process.

(b) If initially there are equal numbers of black-coated and white-coated cats, and no grey-coated cats, what percentage of the next generation will be grey-coated?

(c) In the long run, what percentage of cats will have black, white and grey coats?

2. ## I hope this helps

I need to rethink my response!

3. there should be a vector that multipies with the transition matrix
P . x1 = x2
but i wasn't sure what that vector should be.
if in the case of your matrix,
i assume the vector equation in question (b) is
0.5 ? as there are equal numbers of black and white cats ? correct me if i am wrong
0.5
0

4. ## idea

the vector should be a 3x1 to be able to multiply with the 3x3 matrix ...
so maybe (0.5 0.6 0.45)?

5. ## however

The matrix i originally posted

0.5 0.5 0
0.2 0.6 0.2
0.1 0.45 0.45

is defined in the question as being a result of each colour interbreeding with white coats ... hmmm a little confusing

6. im sure you got the transition matrix right, but i dont understand why
...............(0.5 0.5 0 )
(0.5 0.5 0)(0.2 0.6 0.2)
..............(0.1 0.45 0.45)
links to the next generation of grey cats