Question

A binary communication system transmits a signal X that is either a +2 voltage signal or a -2 voltage signal. A malicious channel reduces the magnitude of the received signal by the number of heads it counts in two tosses of a coin. Let Y be the resulting signal (a) Find the sample space. (b) Find the set of outcomes corresponding to the event transmitted signal was defi- nitely +2." (c) Describe in words the event corresponding to the outcome Y = 0.​

Answer 1

Answer:

1. (10 points) A binary communication system transmits a signal X that is either a +2 voltage signal or a -2 voltage signal. A malicious channel reduces the magnitude of the received signal by the number of heads it counts in two tosses of a coin. Let Y be the resulting signal For example, if both tosses are heads, Y X+ 2, e.g., if X was -2 volt or 2 volt, Y would be 0 volt (a) (4 pts) Observing the value of Y, find the sample space (b) (3 pts) Find the set of outcomes in the event "transmitted signal was definitely +2 (c) (3 pts) What can you infer about X if outcome Y 0? ."

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