Let us consider A$.$ A$.$ Markov's original application of his chains. Given a body of text consider the Markov chain with two states, vowels and consonants. We will analyze the transtion probabilities of vowels to consonants of one of William Shakesphere's poems.

$1)$ Compute the

$-$matrix transition matrix markov$\_$matrix for the above Markov chain.

$2)$ Compute the steady state vector of this system

$3)$ Starting at a consonant, what is the probabilty that the third letter after it is a vowel?

The setup code gives the following variables:

Name Type Description power$\_$iteration function Helper function that performs power iteration poem string The poem to analyze isVowel function Helper function that returns true if the input character is a vowel

Your code snippet should define the following variables:

Name Type Description markov$\_$matrix numpy array Transition matrix steady$\_$state numpy array Steady state vector prob$\_$consonant$\_$to$\_$vowel$\_3$ float Probability