Final answer:
To find the source entropy for three symbols with probabilities of 0.2, 0.7, and 0.1, use the entropy formula H = - ∑ p(i) × log2(p(i)). The calculated source entropy is approximately 1.15677 bits.
Step-by-step explanation:
To calculate the source entropy when a source emits three symbols with probability p1 = 0.2, p2 = 0.7, and p3 = 0.1, we use the formula for the entropy of a source, which is given by:
H = - ∑ p(i) × log2(p(i))
Where p(i) represents the probability of each symbol emitted by the source and the summation (∑) is over all symbols.
Applying this formula:
H = - (p1 × log2(p1) + p2 × log2(p2) + p3 × log2(p3))
H = - (0.2 × log2(0.2) + 0.7 × log2(0.7) + 0.1 × log2(0.1))
Calculating the values we get:
H = - (0.2 × (-2.32193) + 0.7 × (-0.51457) + 0.1 × (-3.32193))
H = - (-0.46439 - 0.36019 - 0.33219)
H = 1.15677 bits
Therefore, the entropy of the source is approximately 1.15677 bits.