A source transmits a message a string of k bits b b1 b2 bk

A source transmits a message (a string of k bits, b = [b_1, b_2, ..., b_k], b_i element {0, 1}, i element {1, ..., k}) through a noisy communication channel. A bit is received incorrectly with probability epsilon (i.e., a transmitted 1 is received as a 0 or a transmitted 0 is received as a 1). Errors in different bit transmissions are independent. In an effort to detect errors, each message will be sent with 1 redundant bit, so that the transmitter sends an n = k + 1 bit packet for each k bit message. The redundant bit is determined in such a way that the number of 1s in the n bit packet is always even. Upon receiving an n = k + 1 bit packet b\' = [b\'_1, b\'_2, ..., b\'_k+1], the receive checks if the number of 1s in the packet is even or odd. If the number of received 1s is odd, then it knows for sure that one or more errors has occurred; however, if the number of received 1s is even, then it cannot know for certain if an error has occurred. Let X denote the number of correctly received bits in the n-bit packet. Calculate the PMF of X. Give an expression for the probability that all n = k + 1 bits are received correctly. If n = 6 and epsilon = 0.1, determine the probability that the receiver detects an error. If n = 6 and epsilon = 0.1, determine the expectation and the variance of X.

Solution

String translation(String temp)
temporary worker.toCharArray();
while(i<k-3)
  
if(storefinal.matches(\"AUU\")||storefinal.matches(\"AUC\")||storefinal.matches(\"AUA\"))

if(storefinal.matches(\"AUG\"))

if(storefinal.matches(\"GUU\")||storefinal.matches(\"GUC\")||storefinal.matches(\"GUA\")||storefinal.matches(\"GUG\"))

if(storefinal.matches(\"UCU\")||storefinal.matches(\"UCC\")||storefinal.matches(\"UCA\")||storefinal.matches(\"UCG\"))

if(storefinal.matches(\"AGA\")||storefinal.matches(\"AGG\"))

if(storefinal.matches(\"AGU\")||storefinal.matches(\"AGC\"))

if(storefinal.matches(\"UGG\"))

if(storefinal.matches(\"UGU\")||storefinal.matches(\"UGC\"))

if(storefinal.matches(\"GAA\")||storefinal.matches(\"GAG\"))

if(storefinal.matches(\"GAU\")||storefinal.matches(\"GAC\"))

if(storefinal.matches(\"AAA\")||storefinal.matches(\"AAG\"))

if(storefinal.matches(\"AAU\")||storefinal.matches(\"AAC\"))

if(storefinal.matches(\"CAA\")||storefinal.matches(\"CAG\"))

if(storefinal.matches(\"CAU\")||storefinal.matches(\"CAC\"))

if(storefinal.matches(\"UAU\")||storefinal.matches(\"UAC\"))

if(storefinal.matches(\"CCG\")||storefinal.matches(\"CCA\")||storefinal.matches(\"CCC\")||storefinal.matches(\"CCU\"))

if(storefinal.matches(\"ACG\")||storefinal.matches(\"ACA\")||storefinal.matches(\"ACC\")||storefinal.matches(\"ACU\"))

if(storefinal.matches(\"GCG\")||storefinal.matches(\"GCA\")||storefinal.matches(\"GCC\")||storefinal.matches(\"GCU\"))

if(storefinal.matches(\"CGG\")||storefinal.matches(\"CGA\")||storefinal.matches(\"CGC\")||storefinal.matches(\"CGU\"))

if(storefinal.matches(\"GGG\")||storefinal.matches(\"GGA\")||storefinal.matches(\"GGC\")||storefinal.matches(\"GGU\"))

if(storefinal.matches(\"UAG\")||storefinal.matches(\"UAA\")||storefinal.matches(\"UGA\"))

i++;
}
String finalreturn = new String(pro);
come finalreturn;
}