1. ## Markov chain

hi

if someone could maybe give me an idea as to how to answer this question please.

I have attached a file with my workings since the formatting is a lot clearer to read.

How do i put all this into a matrix?, i mean i have 10 probabilities only the hint suggests the matrix is 6*6??

help appreciated..

hi

if someone could maybe give me an idea as to how to answer this question please.

I have attached a file with my workings since the formatting is a lot clearer to read.

How do i put all this into a matrix?, i mean i have 10 probabilities only the hint suggests the matrix is 6*6??

help appreciated..
List the possible states at a generation and lable them,

Thus we could take state:

1: aa,aa
2: aa,ab
3: aa,bb
4: ab,ab
5: ab,bb
6: bb,bb

Thus our state vector $\displaystyle x$ is six dimensional with the probability of the state
$\displaystyle i$ being $\displaystyle x_i$.

Now we need to compile the transition matrix $\displaystyle A$, where $\displaystyle A_{i,j}$ is the probability
of ending in state $\displaystyle i$ when we start in state $\displaystyle j$.

An absorbing state is one which once you get into it you cannot leave it, so
from what we know about the model we know that state 1:aa,aa and state
6: bb, bb are absorbing, and the associated element of $\displaystyle A$ corresponding to
the transitions from 1 to 1 is $\displaystyle 1$, and from 6 to 6 is also $\displaystyle 1$.

RonL

3. Originally Posted by CaptainBlack
List the possible states at a generation and lable them,

Thus we could take state:

1: aa,aa
2: aa,ab
3: aa,bb
4: ab,ab
5: ab,bb
6: bb,bb

Thus our state vector $\displaystyle x$ is six dimensional with the probability of the state
$\displaystyle i$ being $\displaystyle x_i$.

Now we need to compile the transition matrix $\displaystyle A$, where $\displaystyle A_{i,j}$ is the probability
of ending in state $\displaystyle i$ when we start in state $\displaystyle j$.

An absorbing state is one which once you get into it you cannot leave it, so
from what we know about the model we know that state 1:aa,aa and state
6: bb, bb are absorbing, and the associated element of $\displaystyle A$ corresponding to
the transitions from 1 to 1 is $\displaystyle 1$, and from 6 to 6 is also $\displaystyle 1$.

RonL
hi Captain Black

do i multiply the probabilities?? e.g. ab,ab = 1/3*1/3*1/3=1/27 ??

hi Captain Black

do i multiply the probabilities?? e.g. ab,ab = 1/3*1/3*1/3=1/27 ??
Your diagrams provide all you need to compute the probabilities.

RonL

5. Originally Posted by CaptainBlack
Your diagrams provide all you need to compute the probabilities.

RonL
im looking at the parents....do i need to be looking at the offspring to construct the matrix??

im looking at the parents....do i need to be looking at the offspring to construct the matrix??
To construct the matrix you need to look at the transition probabilities from each parent state to offspring state.

RonL

7. Originally Posted by CaptainBlack
To construct the matrix you need to look at the transition probabilities from each parent state to offspring state.

RonL
im trying that, only it's confusing the hell out of me..:-), i mean for a matrix..

ab bb aa

aa

ab

bb

im not a statistical person but...all parents.... and the probs just dont fit....

ab bb aa is supposed to represent the top row

8. Originally Posted by CaptainBlack
To construct the matrix you need to look at the transition probabilities from each parent state to offspring state.

RonL

well they all sum to 6, do i scale them down to sum(p: x,y,z)=1??

i just dont get it!!

ditto

now we need a transition matrix A, where A_i,j is the probability of ending in state i given we start in state j.

from 4: ab,ab, possibilities for offspring are: aa,bb or ab and we have to repeat the process for all offspring. This gives us

1. aa,bb,ab
2. bb,aa,ab
3. ab,aa,bb
4. ab,bb,aa
5. aa,ab,bb
6. bb,ab,aa

the above possibilities.

am i right to say that the selected offspring being also ab,ab, is (1/2*1/2*1/2)+(1/2*1/2*1/2)+...+(1/2*1/2*1/2) six times, or 6(1/8)??

And will my matrix need to be a 6*6 with aa,aa,ab,ab,bb,aa for rows and aa,ab,ab,bb,bb,bb for cols (in any order)??
thanks

help appreciated..