a) A 2-bit binary sequence is transmitted over a noisy communication channel. The noise corrupts the signal in the sense that a transmitted digit transmitted can be flipped with probability 0.2. It has been observed that, across a large number of transmitted signals, the 0s and 1s are transmitted in the ratio 2:3. Given that the sequence 10 is received, calculate the probability that this sequence was transmitted. b) A random variable X has a mean EX] = 1 and variance Var(X] = 1. i) Find P[X 2 2] if X has an exponential distribution. ii) Find P[X 2 2] if X has a normal distribution. iii) Find P[X 2 2] if X has a uniform distribution. iv) Find an upper bound for P[X 2 4], if nothing else is known about the distribution of X but the mean and variance