An experimental PSK signaling system has two channels through which design engin

Question

An experimental PSK signaling system has two channels through which design engineers are sending randomly-generated bits. Channel #1 outputs the bit 0, 70% of the time. Channel #2 outputs the bit 0, 90% of the time. An experiment will start by sending the first bit through Channel #2. If the first bit through that channel is a 0, then a second bit will be sent through that same channel. However, if the first bit is a l, then the next bit will be sent through Channel #1. What is the probability that the order of the bits at the system's output will be 1, 1,0,0, 1? (25 points)

Explanation / Answer

we have to find the system's output shall be 1,1,0,0,1

so We will receive first output : Pr(first output of 1 from channel 2) = 1 - 0.9 = 0.1

Now we will change chennel

Pr(second output is 1) = Pr(first channel will send output 1) = 1- 0.7 = 0.3

Now channel will be changed again

Pr(third output is 0) = Pr(second channel will send output 0) = 0.9

No channel will be changed

Pr(Fourth output is 0) = Pr(second channel will send output 0) = 0.9

no channel will be changed

Pr(fifth output is 1) = Pr(second channel will send output 1) = 0.1

Total probability of achieivng that output is = 0.1 * 0.3 * 0.9 * 0.9 * 0.1 = 0.00243

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