Suppose that for some event that has not yet occurred we can expect to get a val

Question

Suppose that for some event that has not yet occurred we can expect to get a value (outcome) for variable x and a value for variable y. The state space (the set of possible outcomes) for variable x is X = {a, b, g} and that the state space for y is Y = {a, b, c, d}. We know the probabilities for each possible outcome for both x and y to be the following: p(a) = 0.20, p(b) = 0.30, p(g) = 0.50, p(a) = 0.10, p(b) = 0.20, p(c) = 0.30, and p(d) = 0.40. a. What are the Hartley information measures I(X) and I(Y) in bits? b. What are the Shannon information measures H(X) and H(Y) in bits? c. Suppose that the joint probabilities of the outcomes are the following what is the information transmission T(X, Y)?

Explanation / Answer

Ans;

(b) Shannon information measures are

H(X)= 0.20 log(0.20) + 0.30 log(0.30) + 0.50 log(0.50) = -0.4472 bits

H(Y)= 0.10 log(0.10) + 0.20 log(0.20) + 0.30 log(0.30) + 0.40 log(0.40) = -0.5558 bits

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.