3. 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 sginal

by the number of the heads it counts in two tosses of a coin. Let Y be the resulting

signal.

(a) Find the sample space for Y.

(b) Find the set of outcomes corresponding to the event "transmitted signal was

denitely +2".

(c) Describe in words the event corresponding to the outcome Y = 0.

My Answer : a) X = { -2 , 2 } as either -2 or +2 voltage level signal is transmitted

Signal gets reduced by Malicious channel as the number of heads we get i.e N = { HH , TH , HT , TT } = { 2 , 1 , 1 , 0 } , therefore signal reduces by N = {2,1,0} , Now Y = X - N = 2,1,0 ( For X = -2 ) or Y= X-N = -2 , -3 , -4 ( For X = -2 ) . therefore Sample Space for Y = { 2,1,0,-2,-3,-4} .

b) B = set of outcomes corresponding to the event that transmitted signal was definitely +2 , i.e X = +2 and Channel reduces it by 2, 1 , 0 , therefore outcomes in Y are 2,1,0 , therefore B = { 2,1,0}

c) event corresponding to outcome Y=0 is : "The Transmitted signal was definitely X= + 2 and the Malicious channel reduces the magnitude of +2 by 2 to obtain Y=0 , due to 2 heads obtained"

These are my answers but it does not match to theirs which are :

Actual Answers :

a) Sample space = { -2, -1 ,0 ,1 , 2 } = how ??

b) B = { 1,2 } , how ?? Shouldn't it be { 0 , 1 , 2 }

c) Y = 0 when X = 2 or X = -2 , hence we cannot determine input signal X , how is this possible ?? It should be X = +2 only and malicious channel reduces by 2 hence 0.

Kindly Explain as i am not able to comprehend this.