Please explain your reasoning to solve this problem. Provide as much details as
ID: 3041381 • Letter: P
Question
Please explain your reasoning to solve this problem. Provide as much details as possible. Thank you! =)
Psoblem In a diital communication sustem, messages are encoded into the. sumbols 0 and 1. Becuse of noise in the suslen nar the incorrect sumbol is Sometimes received. Suppose at he bailiyof beiny ronsmited is 0.4, and the grobabilty of 1 being transmitted is 0.6. urther sugpose that if a 0 is transmitted, hen the babil Tf a is transmitted, then he probability receiving a 1 is 0.02 receivina, a 0 is 0.05. Q) the received s2mbol is 0, what is the robabil b) If the received symbol is1, uhat is the probability that the tansmited (c) Whot is he probability hat the received symbol is 1? at the transmited Sumbol is 0 Sumbol is a 1? If the received symbol is 1 what is the robabilit , that the transmitted sumbol is a 0Explanation / Answer
a) probability of receiving 0 =P(0 transmitted and 0 receivd+1 transmitted and 0 receivd)
=0.4*(1-0.08)+0.6*0.05 =0.398
hence probability of transmitting 0 given received 0=P(0 transmitted and 0 receivd)/P( receiving 0)
=0.4*(1-0.08)/0.398=0.9246
b)
probability of receiving 1 =P(1 transmitted and 1 receivd+0 transmitted and 1 receivd)
=0.6*(1-0.05)+0.4*0.08=0.602
hence probability of transmitting 1 given received 1=P(1 transmitted and 1 receivd)/P( receiving 1)
=0.6*(1-0.05)/0.602 =0.9468
c) probability of transmitting 1=P(1 transmitted and 1 receivd+0 transmitted and 1 receivd)
=0.6*(1-0.05)+0.4*0.08=0.602
d)
robability of transmitting 0 given received 1=P(0 transmitted and 1 receivd)/P( receiving 1)
=0.4*0.08/0.602 =0.0532