hope you are doing well. So I was asked to design and conduct a simulation study to estimate the probability that the observed maximum run length (A run is a sequence of consecutive heads or tails) for a fair coin flipping experiment is in the interval [9, 11] in a sample size of n = 1000, this is my attempt so far

```
result <-replicate(10000,{ #replicate 10000 times
experiment <- sample(c("T","H"),size=1000,replace=TRUE) #1000 flips
expe_run <- rle(experiment) #find the run
expe_val <- expe_run$values #values of run
expe_length <- expe_run$lengths #length of run
as<-list(expe_length,expe_val) #make a list for sapply function
max_run <-sapply(as, FUN=max) #apply max function through out for both
head_run <-expe_length[which(expe_val=='H')] # show the head run
tail_run <-expe_length[which(expe_val=='T')] #show the tail run
max_run
})
probability <-table(result)/10000 #probability for run probability
```

The problem is I don't know how to finish the question, which is estimates the probability that the observed maximum run length for a fair coin flipping experiment is in the interval [9, 11], even though I got the table for every possible probability. Can you please help me out? Thank you