Use MATLAB to build a simulation of Quiz 2.3. Simulate the transmission of 10000 packets, each containing 100 bits. Count the number of packets that contain no error, one, two, three-bit errors, calculate their probabilities. Also calculate the probability of a packet is decoded correctly. Compare your numbers from MATLAB with your theoretical calculation.

YOU MUST USE MATLAB TO SOLVE. THANK YOU!

Data packets containing 100 bits are transmitted over a communication link. A transmitted bit is received in error (either a O sent is mistaken for a 1, or a 1 sent is mistaken for a 0) with probability0.01, independent of the correctness of any other bit. The packet has been coded in such a way that if three or fewer bits are received in error, then those bits can be corrected. If more than three bits are received in error, then the packet is decoded with errors. (a) Let Ek, 100-k denote the event that a received packet has k bits in error and 100 - k correctly decoded bits. What is P[Ek, 100-kl for k0,1,2,3? (b) Let C denote the event that a packet is decoded correctly. What is P[C]? Quiz 2.3 Solution (a) In this problem, k bits received in error is the same as k failures in 100 trials. The failure probability is 1-p and the success probability is 1_-P. That is, the probability of k bits in error and 100-k correctly received bits is P100-400)()o-4 (1- E) For e 0.01 (0.99)1000.3660 0,100(1- e P |E1.99-100(0.01)(0.99)99-0.3700. P |E2.98] = 4950(0.01)2(0.99)98 = 0.1849. P E397161,700 (0.01)(0.99)0.0610. 4 (b) The probability a packet is decoded correctly is just