(10 points) A binary communication system transmits a signal X that is either a +2 volt signal or a 2 volt 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, and X was 2 volt or 2 volt, then Y would be 0 volt; if X was 2 volt, and only one head in the two tosses, then Y would be 1 volt. (a) (4 pts) Observe the value of Y, and find its sample space (i.e., all possible values of Y ). (b) (4 pts) Find the set of outcomes (i.e., possible values of Y ) in the event "transmitted signal X was definitely 2." (c) (2 pts) If outcome Y=0, list all possible values of X