```
library(markovchain)
data("preproglucacon", package = "markovchain")
= preproglucacon$preproglucacon
x
head(x)
```

`[1] "G" "T" "A" "T" "T" "A"`

Avery and Henderson (1999) discusses the use of Markov chains in modeling DNA sequences (in the preproglucacon protein). The data set `preproglucacon`

in the `markovchain`

package contains related data.

```
library(markovchain)
data("preproglucacon", package = "markovchain")
= preproglucacon$preproglucacon
x
head(x)
```

`[1] "G" "T" "A" "T" "T" "A"`

- Use the data to estimate the transition matrix.
- Find and interpret a 95% confidence interval for \(p(A, C)\).
- Find the stationary distribution that corresponds to the estimated transition matrix.
- Find the observed relative frequency of each state in the data. How do the observed relative frequencies compare to the stationary distribution?
- Create an appropriate plot to assess if the observed sequence can be reasonably considered an observation from a (first order) Markov chain.
- (Optional.) Use the
`markovchain`

package to test if the observed sequence can be reasonably considered an observation from a (first order) Markov chain