$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by: $P(X=0,Y=0)=0.06$ $P(X=0,Y=1)=0.14$ $P(X=1,Y=0)=0.24$ $P(X=1,Y=1)=0.56$ The mutual information $I(X;Y)$ is ______ (rounded off to two decimal places). 0.00[c] 1.00 0.50 0.25 1 1/3 mcq Computer Science And Engineering Engineering Mathematics The mutual information is calculated using: $$ I(X;Y)=\sum p(x,y)\log_2\frac{p(x,y)}{p(x)p(y)} $$ Marginal probabilities: $P(X=0)=0.2$, $P(X=1)=0.8$ $P(Y=0)=0.3$, $P(Y=1)=0.7$ For every combination: $$ \frac{p(x,y)}{p(x)p(y)}=1 $$ Therefore, $$ \log_2(1)=0 $$ Hence all terms become zero and: $$ I(X;Y)=0.00 $$

GATE - Subject-wise PYQ | GEC Wayanad Question Bank

$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$ . The joint probability mass function of the random variables is given by:

$P(X=0,Y=0)=0.06$

$P(X=0,Y=1)=0.14$

$P(X=1,Y=0)=0.24$

$P(X=1,Y=1)=0.56$

The mutual information $I(X;Y)$ is ______ (rounded off to two decimal places).

0.00[c]

1.00

0.50

0.25

1/3

mcq

Computer Science And Engineering

Engineering Mathematics

The mutual information is calculated using:

I(X;Y)=\sum p(x,y)\log_2\frac{p(x,y)}{p(x)p(y)}

Marginal probabilities:

$P(X=0)=0.2$ , $P(X=1)=0.8$

$P(Y=0)=0.3$ , $P(Y=1)=0.7$

For every combination:

\frac{p(x,y)}{p(x)p(y)}=1

Therefore,

\log_2(1)=0

Hence all terms become zero and:

I(X;Y)=0.00