I am interested in finding the estimated number of characters for a monkey to randomly type ABCDAE.
Keyboard in question is 26 keys (English alphabet) with independence and uniform probability.
I understand how probabilities of progressing from each state can be found from Markov chains, i.e. how typing an A at the 2nd/3rd/4th/6th position of the string will only require BCDAE to be typed subsequently.
However I am confused with how to use generating functions to find the expected characters before this is typed.
Any resources or working through this would be appreciated!
Thanks