Question

7. Binary signals are transmitted at a constant rate of 1000 per second. Suppose trans- mission errors occur independently with a probability of 0.15. Using this information, answer the following questions. (a) What is the probability that there are 1 or more transmission errors in 3 seconds? (4 points) (b) Provide an approximation of the probability that there are 500 or more trans- mission errors in 3 seconds. (Hint: Finding the exact probability is very time consuming, hence you are being asked to find an approximate value. (8 points) (c) Let Q denote the number of transmissions till the 3rd transmission error occurs. What is the distribution of Q? (3 points)

Answer 1

The three transmission errors moyen occurred in at three or more binary signals transmilted. Hence a can take the values 3,4,5 – – PLQ=3) = P(Q=4) 0.15 0.15 0.15 [all three are errors] = 0.15) (0.85) [3 tror errors, one cabo dubithout exors] 2-2 P (Q=)) = (0.15) (0.85) . [3 errors and n.3 without error] Benue P(@= k) = Co.1532(0.853k-3 distribution of ha"