The.entropy of a discrete random variable X Is H(X). If another discrete random variable Y is defined as Y= 4X, then the entropy of Y, i.e: H(Y)will be equal to

H(X) + 2

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2H(X)

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H(X)

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4H(X)

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Solution

The correct option is C H(X)
$H (X) = - \sum_{i = 1}^{N} P (x_{i}) l o g_{2} P (x_{i})$
Y = 4X
$f_{Y} (y) = f_{X} (x) \frac{d X}{d Y} = \frac{4 X}{4}$
$f_{Y} y = X$
$P (y_{i}) = P (x_{i})$
H(Y) = H(X)

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Similar questions

I f X a n d Y a r e t w o d i s c r e t e r a n d o m v a r i a b l e s a n d H (V) r e p r e s e n t s t h e e n t r o p y o f t h e v a r i a b l e V, t h e n c o n s i d e r t h e f o l l o w i n g r e l a t i o n s : S e l e c t t h e c o r r e c t r e l a t i o n s u s i n g t h e c o d e s g i v e n b e l o w . R 1 : H (X) \geq H (X | Y) R 2 : H (X, Y) \geq H (X) + H (Y) R 3 : H (x) - H (Y) = H (X | y) - H (Y | X)

μ_{2} = 20, μ_{2}^{1} = 276

X

X

\frac{1}{2} 1 \frac{3}{2} 2

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