- #1
SamTaylor
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Homework Statement
A Communication system transmits signals labeled 1, 2, and 3. The probability
that symbol j is sent and symbol k is received is listed in the table for each
pair (j,k) of sent and received symbols. For example, the probability is 0.12
that a 1 is sent and, owning to noise in the channel 3 is received.
Calculate the probability that the symbol k was sent, given that symbol k is
received, for k = 1,2,3, and calculate the probability of error incurred in
using this system. An Error is defined as the reception of any symbol other
than the one transmitted.
Homework Equations
1
[tex]P(B|A)=\frac{P(A|B)*P(B)}{P(A)}[/tex]
2
[tex]P(M)=P(A)*P(M|A) + P(B)*P(M|B) + P(C)*P(M|C)[/tex]
The Attempt at a Solution
Problem 1: Symbol k was sent, given that k is received
[tex]P = P_{11} + P_{22} + P_{33}[/tex]
Problem 2: Probabilty of Error
[tex]P_e = P - 1[/tex]
Or do the numbers inside the table represent conditional probabilitys?
P(received|send) ... for example P(3|1) = 0.12