On Thu, 15 May 2014 10:03:03 AM chantel7777777 wrote: Dear Chantel, The problem: A perplexed student decides to post her/his (note non-sexist usage) homework to the R help list on a Friday evening. On Monday morning, she finds that she/he has received five different answers. Realizing that some might be incorrect, she/he persuades her/his smart friend to check them. Sadly, the friend, while very smart, is also very lazy and only does one now and then. The probabilities of the number of the answers judged incorrect each day are:
Incorrect Probability 0 0.25 1 0.3 2 0.25 3 0.2 Whenever she/he gets this information, she/he strikes off those answers from the list. If she/he has one or no remaining answers at the end of each day, she/he posts the question to the R help list that evening, and receives five more answers the next morning. What is the most probable value for the number of remaining answers that she/he will have on Friday morning? First you need the transition matrix. Assuming that the steps are from morning to morning: pmat<- matrix(c(0.25,0,0,0.45,0.3, 0.3,0.25,0,0.2,0.25, 0.25,0.3,0.25,0,0.2, 0.2,0.25,0.3,0.25,0, 0,0.2,0.25,0.3,0.25), nrow=5,ncol=5,byrow=TRUE) rownames(pmat)<-colnames(pmat)<-2:6 pmat Since she/he began with five answers, we begin with state 4. Notice here that since each step is from morning to morning and the R help list is amazingly reliable, there are no 0 or 1 states. initstate<-c(0,0,0,1,0) One method of calculating the distribution after a number of steps is to multiply the initial state by the transition matrix raised to the power of the number of steps, so: initstate%*%pmat%*%pmat%*%pmat%*%pmat While this produces the correct answer, it is not the correct method. You want to collect a number of probabilistic outcomes and use this to estimate the most likely value of the number of potential answers remaining on Friday morning. outcomes<-rep(NA,100) for(round in 1:100) { start=4 for(i in 1:4) start<-sample(1:5,1,prob=pmat[start,]) outcomes[round]<-start } table(outcomes) So our hypothetical student might be able to work out from this how to correct her/his code. Jim ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.