Question

Prob.4 A digital transmission system sends strings of binary (0 or 1) bits through the channel to the receiver. Assume that the probability of a bit error in the channel is 10-2 and that a string of 1000 bits is transmitted (a) Calculate the probability that more than three bit errors will occur in the 1000 transmissions (b) Use the Poisson approximation to calculate the probability that more than three bit errors wil occur in the 1000 transmissions.

Answer 1

Given probabiihy of bit em ar P- 152 O O Tumber o bits tangmitted - lo00. Tamdem Vaiable ohoge Voalune Tepregen a) het be a -ts nuber o errors Probeabiting dhat mare than 3 bit esTs uil1oCer in the looo tfommiggie) is - PCx=) tpO=)+Px=2)+PCx=3) P(x 000 999 p0c, Co0 (-00) +lo0c, o(-o-0) PCx>) 998 (-0o) +1003 (оо) (-00) 3 + 1o0 C, (oo PCA3)=0.9899 (b Ihe mean of Poiom Rande Vojakole P = (o00)(0.0) 1o PCx-+pCx= )+PCx= 2)+P(x P(x3) 10 e -10- (16) -10 е (10) 2 2 (16) 1 - 31 P(x73) = 0.9896