# Re: [R] statistics help

From: Ingmar Visser <I.Visser_at_uva.nl>
Date: Fri 24 Nov 2006 - 09:46:06 GMT

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@hotmail.com>
> Date: Thu, 23 Nov 2006 19:07:54 +0000
> To: <r-help@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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