Estimate how many patterns in AY are recognizable as the character ‘2'. [The aim of this problem is to try to demonstrate the existence of as many patterns as possible that are recognizable as 2s.]

Discuss how one might model the channel P(y | x=2). Estimate the entropy of the probability distribution P(y | x=2)
One strategy for doing pattern recognition is to create a model for P(y | x) for each value of the input x = {0, 1, 2, 3, . . . , 9}, then use Bayes' theorem to infer x given y.

This strategy is known as full probabilistic modelling or generative modelling. This is essentially how current speech recognition systems work. In addition to the channel model, P(y | x), one uses a prior probability distribution P(x), which in the case of both character recognition and speech recognition is a language model that specifies the probability of the next character/word given the context and the known grammar and statistics of the language