1
GATE ECE 2017 Set 1
Numerical
+1
-0
Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_2}$$ has mean 1 and variance 4. The mutual information I $$\left( {{X_1},\,{X_2}} \right)$$ between $${{X_1}}$$ and $${{X_2}}$$ in bits is ________________.
2
GATE ECE 2016 Set 3
Numerical
+1
-0
An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $${p_1}$$ = $${p_4}$$ = 0.125 and $${p_2}$$ =$${p_3}$$. The information rate (bits/sec) of the message source is ____________________
3
GATE ECE 2016 Set 2
Numerical
+1
-0
A discrete memoryless source has an alphabet $$({a_1},\,{a_2},\,{a_3},\,{a_4})\,$$ with corresponding probabilities$$\left( {{1 \over 2}\,\,,{1 \over 4},\,{1 \over 8},\,\,{1 \over 8}\,} \right)$$. The minimum required average codeword length in bits to represent this source for error-free reconstruction is__________________________
4
GATE ECE 2012
+1
-0.3
A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount $$\varepsilon$$ and decreases that of the second by $$\varepsilon$$. After encoding, the entropy of the source
A
increases
B
remains the same
C
increases only if N = 2
D
decreases
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