From the given table, determine the Entropy (H)Symbol Probability Time of TransmitX0 0.3 18 µsecX1 0.25 17 µsecX2 ? 22 µsecExpress your answer in 4 decimal places.
Question
From the given table, determine the Entropy (H)Symbol Probability Time of TransmitX0 0.3 18 µsecX1 0.25 17 µsecX2 ? 22 µsecExpress your answer in 4 decimal places.
Solution
To calculate the entropy (H), we first need to know the probability of X2. Since the total probability must equal 1, we can calculate the probability of X2 as follows:
P(X2) = 1 - P(X0) - P(X1) = 1 - 0.3 - 0.25 = 0.45
Entropy (H) is calculated using the formula:
H = - ∑ [ P(x) * log2 P(x) ] for all x
So, we substitute the probabilities into the formula:
H = - [ P(X0) * log2 P(X0) + P(X1) * log2 P(X1) + P(X2) * log2 P(X2) ]
H = - [ 0.3 * log2(0.3) + 0.25 * log2(0.25) + 0.45 * log2(0.45) ]
Now, calculate the values:
H = - [ 0.3 * (-1.737) + 0.25 * (-2) + 0.45 * (-1.152) ]
H = - [ -0.521 + -0.5 + -0.518 ]
H = 1.539
So, the entropy (H) is 1.539 (to 4 decimal places).
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