GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 31 of 65

Marks: +1, -0

A binary random variable

X

takes the value

+2

-2 .

The probability

P(X=+2)=a

. The value of a (rounded off to one decimal place), for which the entropy of

X

is maximum, is

Solution:

There are only two symbols

X=-2

{X}=2

Maximum entropy occurs for equal probability

{H}( {X})_{\max }=\log _{2}^{2}=1

P(X=2)=\;{1}/{2}

P(X=-2)=\;{1}/{2}

Go to Question:

Prev Question

Next Question