A discrete memoryless source produces 3 independent symbols with probabilities 12-14 and 14- The entropy of the 4th order extensioni-e- 4 symbols as one block of this source is bits-block-

Entropy of the source. nbsp; H(X)= ∑_i=0^2P(x_i)log_2P(x_i) =12log_2(2)+14log_2(4)+14log_2(4) bits/symbols =12+24log_2(4) bits/symbol =1.5 bits/symbol Entropy ...

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Standard XII

Mathematics

Properties of Determinants

A discrete me...

Question

A discrete memoryless source produces $3$ independent symbols with probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ . The entropy of the 4th order extension
(i.e., 4 symbols as one block) of this source is ____ bits/block.
6

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Solution

The correct option is A 6
Entropy of the source.
$H (X) = - 2 \sum i = 0 P (x_{i}) l o g_{2} P (x_{i})$
$= \frac{1}{2} l o g_{2} (2) + \frac{1}{4} l o g_{2} (4) + \frac{1}{4} l o g_{2} (4)$ bits/symbols

$= \frac{1}{2} + \frac{2}{4} l o g_{2} (4)$ bits/symbol $= 1.5$ bits/symbol
Entropy of the $4^{t h}$ order extension of the source is,
$H (X^{4}) = 4 H (X) = 4 (1.5)$ bits/block $= 6$ bits/block

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A discrete memoryless source produces 3 independent symbols with probabilities 12,14 and 14. The entropy of the 4th order extension (i.e., 4 symbols as one block) of this source is ____ bits/block.6

The correct option is A 6Entropy of the source. H(X)=−2∑i=0P(xi)log2P(xi) =12log2(2)+14log2(4)+14log2(4) bits/symbols =12+24log2(4) bits/symbol =1.5 bits/symbol Entropy of the 4th order extension of the source is, H(X4)=4H(X)=4(1.5) bits/block =6 bits/block

A discrete memoryless source produces $3$ independent symbols with probabilities $\frac{1}{2}, \frac{1}{4}$ and $\frac{1}{4}$ . The entropy of the 4th order extension
(i.e., 4 symbols as one block) of this source is ____ bits/block.
6