[R] statistics help

[Ingmar Visser]

Dear Rohan, 
Why would you want to simulate these probabilities? As far as I can tell by
your description these are all solvable analytically, see eg Kemeney,
Mirkil, Snell & Thompson, 1958, Finite Mathematical Structures. There are
undoubtedly more recent publications that cover first passage times in
Markov models, which is what you are looking for.
Hth, Ingmar

> From: Rohan Saldanha <rohansaldanh at hotmail.com>
> Date: Thu, 23 Nov 2006 19:07:54 +0000
> To: <r-help at stat.math.ethz.ch>
> Subject: [R] statistics help
> 
> hi
> 
> im a bioinformatics student as i have never had any previous programming
> experience
> i need help
> 
> this is the question i need to answer:
> 
> Random walk model
> 
> we want to model a random walk where you take a step to the left with
> probability p
> and one to the right with probability 1-p. Now assume that there is a line
> of 11 squares.
> once you are in square 0 or in square 10 the walk ends. The aim of this
> problem set is
> to write a simulation for the random walk and analyse its dynamics
> 
> 1. write a simulation for a random walk which allows you to calculate the
> probability of ending
>      up in square 0 starting from any other square.
> 
> 2. analyse the probability of ending up in square 0 starting from any other
> square. Also calculate the mean time until you have reached square 1 for p=
> 0.1,0.2,0.3,0.4 and 0.5. What is the probability of reaching square 10 for
> these parameters
> hint simulate each scenario 1000 times and plot on histogram
> 
> 
> this is the code that i have come up with but its not working very well.
> 
> rw<-function(sw,p,nrep){
> Z=0
> T=0
> count=0
>        for (i in 1:nrep)
>    {
>       n<-0
>       s=sw
> 
>       while (s>0 & s<10)
>      {
>          x<-runif(1, min=0, max=1)
>          if (x<p) {s<-s-1}
>          else{s<-s+1}
>          print (s)
>          n<-n+1
>      }
>      count<-count+n
>      print (count)
> 
>      if (s==0) {Z<-Z+1}
>      else {T<-T+1}
>    }
>      PrZ=Z/nrep
>      print(c("PrZ",PrZ),quote=FALSE)
> }
> 
> if you could shed some light on this it woul be really helpful. please let
> me know how much
> you would like as payment aswell.
> 
> thanks
> rohan
> 
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