Let us consider the detection of the framing bit in the T1 carrier by the receiver. Assume that the data bits in a frame assume values of 1 and 0 with equal probabilities of 0.5 and independent of each other. The framing bit alternates between 1 and 0 values.
i) Determine probability distribution of the number of trials that it will take for the receiver to determine that tested bit is not the frame bit ( Show your work).
ii) When a tested bit fails the receiver starts testing the bit in the position next to the failed bit as in part i). Determine the probability distribution of the number of times that the test in part i) will be repeated until the framing bit is determined.