You are Here: Home >< Maths

# probability watch

1. I'm not sure how I would go about doing this one:

For 0<a<1 and 0<b<1 consider the matrix:

Show that for any n>=0,

Any help would be much appreciated
2. (Original post by Goldenratio)
I'm not sure how I would go about doing this one:

For 0<a<1 and 0<b<1 consider the matrix:

Show that for any n>=0,

Any help would be much appreciated
Could you not show that it's true by induction?? I'm just glancing at it, but show it's true for the case n=1, then assume it's true for the case of n, and show that it's true for the case n+1, and then it should hold true for all n. That's a bit of a guess, but I think it would work!!
3. erm does it make any difference if it is a stochastic matrix?
4. I've just done it by induction (I think!!), and it's quite messy, but took only 20 minutes. I haven't done Markov Chains yet, so I can't be sure that it's the easiest method (in fact, it most probably isn't!!). Hope it all goes well!!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 23, 2006
Today on TSR

### Cambridge interviews

Find out which colleges are sending invitations

### University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams