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Problem 4. Messages arrive at a node in a communication system. A message is corrupted by noise with probability p-005. Let X be the number messages until the first message in error is read. How would you justify the clain that X is a geometric random variable with parameter p 0.05

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Answer #1

Here each massage arrive at a node in a communication system independently.

Also the probability of the message is corrupted by noise = 0.05 which is constant for each trials.

The experiment is continue until we get first message in error is read.

So if X is the number of trials required to get  first message in error is read then X take values as 1, 2, 3, ....

That is n, the sample size is not fixed.

So X follows all the assumptions of the geometric distribution with parameter po = 0.05

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