Question

In a communication system, packets are transmitted from a sender to a receiver. Each packet is received with no error with probability p independently from other packets (with probability 1−p the packet is lost). The receiver can decode the message as soon as it receives k packets with no error. Compute the probability that the sender sends exactly n packets until the receiver can decode the message successfully

Answer 1

Answer:

Given that

Each packet is received with no error with probability p independently from other packets (with probability 1−p the packet is lost).

The receiver can decode the message as soon as it receives k packets with no error.

To Compute the probability that the sender sends exactly n packets until the receiver can decode the message successfully:

For the situation where thereceiver decode as soon as possible, the packets receiver by him without mistake should exactly be k out of n packets.

Likewise , just two possibilities are there those are Failure or success, it behaves on like a binomial distribution.

Therefore the probability that the sender sends exactly n packets until the receiver can decode the message successfully is P( X= K) = nCk * (p)^k * (1-p)^(n-k).