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 3 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 definitely
-2”.
c) Describe in words the event corresponding to the outcome Y = 1.
d) Use a tree diagram to find the set of possible input-output pairs.
e) Find the probabilities of the input-output pairs.
f) Find the probabilities of the output values.
g) Find the probability that the input was X = -2 given that Y = k.