I have an urgent problem but I'm a little lost.

Is this probability question referring to the use of Bayes' theorem?

Consider a language with only two symbols I and O. The proportion pI of

the symbol I in the language is unknown. Suppose one particular sample text consists of a sequence of N symbols drawn randomly and independently from the language, out of which the symbol I occurs NI times and the symbol O occurs N – NI times in this

particular sample text.

(a) Write an expression for the probability of the sample text in terms of pI, NI, and N.

(b) Derive mathematically the value of pI that maximizes the probability of the sample

text, in terms of NI and N. This value serves as an estimate of pI.

the symbol I in the language is unknown. Suppose one particular sample text consists of a sequence of N symbols drawn randomly and independently from the language, out of which the symbol I occurs NI times and the symbol O occurs N – NI times in this

particular sample text.

(a) Write an expression for the probability of the sample text in terms of pI, NI, and N.

(b) Derive mathematically the value of pI that maximizes the probability of the sample

text, in terms of NI and N. This value serves as an estimate of pI.

P(I) = Ni/N, P(O) = (N - Ni)/N, do we now multiply the two together? Then where does the original pI figure in?

And what is part (b) dealing with? Is it in trying to estimate the prior? Does this mean something like arg max P(I | O)P(I)? My mind keeps going round in circles in this!

Please help!