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.