Chapter 3 homework assignments

3.1 An upper layer message is split into 10 frames, each of which as an 80 percent chance of arriving undamaged. If no error control is done by the data link protocol, hoe many times must the message be sent on the average to get the entire thing through?

Ans: This is a repeated experiment. The probability of successful transmission of one frame is, pf = 0.8 but the probability of doing this 10 times in a row is p==probability of getting a message through. Why?

Because the message will only be successful if all of the frames are successful. The probability of not getting the message through is 1-p.

Suppose you repeat the trials 10 times. This means that you failed 9 times but succeeded once. The exact probability of this happening is:

OK! Now what is the expected (or average) number of trials? Recall that expectation is given by:

So that

This is a sum of an infinite series. Here are a couple you might like to help simplify the above:

And the derivitave which is given by:

You should be able to solve for E(x) now