Is Y2+Y3 independent of Y1? NO!
Is Y2−Y3 independent of Y1? YES!
A binary communication system is used to send one of two messages:
(i) message A is sent with probability 2/3, and consists of an infinite sequence of zeroes,
(ii) message B is sent with probability 1/3, and consists of an infinite sequence of ones.
The ith received bit is “correct" (i.e., the same as the transmitted bit) with probability 3/4, and is “incorrect" (i.e., a transmitted 0 is received as a 1, and vice versa), with probability 1/4. We assume that conditioned on any specific message sent, the received bits, denoted by Y1,Y2,… are independent.
Is Y2+Y3 independent of Y1?
Is Y2−Y3 independent of Y1?
2 answers
1. Is Y2+Y3 independent of Y1?
NO
2.Is Y2−Y3 independent of Y1?
YES
NO
2.Is Y2−Y3 independent of Y1?
YES
8 answers