Question: Question 3 a) A 2-bit binary sequence is transmitted over a noisy communication channel. The noise corrupts the signal in the sense that a transmitted

Question 3 a) A 2-bit binary sequence is

Question 3 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 0.15. It has been observed that, across a large number of transmitted signals, the Os and 1s are transmitted in the ratio 1:3. Given that the sequence 00 is received, calculate the probability that this sequence was transmitted. b) Suppose X and Y are random variables such that E[X1=1, a=1, E[Y=2, 3=2, Cov[X,Y)=2. Compute the following quantities: (1) E[X + 2Y). (ii) The correlation Rxy. (iii)Var(2X+Y). (iv) Are X and Y correlated? Why

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