QUESTION 3 (a) Consider the code C={0,1} as the input to a binary symmetric channel with bit-error probability 0.1. (i) What is the lowest achievable probability of mistake, if the receiver does not know the input probability distribution (po 1-po]? Discuss. What detection rule should the receiver use? (ii) What is the lowest achievable probability of mistake, if the receiver knows that the probability distribution of the input is [0.99 0.01]? Discuss. What detection rule should the receiver use? (b) Suppose we issue ID numbers in the form of strings of 13 bits to all students in a study programme, using a 1-error correcting code. What is the maximum possible number of students in the study programme