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GATE EC 2016 Set 2 — Question 61

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NAT+2 / -0HardConditional ProbabilityProbabilityEngineering MathematicsInformation Measure & EntropyInformation TheoryCommunications

Communications → Information Theory → Conditional Probability

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Question

A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events:
x0x_0 : a "zero" is transmitted
x1x_1 : a "one" is transmitted
y0y_0 : a "zero" is received
y1y_1 : a "one" is received
The following probabilities are given: P(x0)=12P(x_0) = \frac{1}{2}, P(y0∣x0)=34P(y_0|x_0) = \frac{3}{4}, and P(y0∣x1)=12P(y_0|x_1) = \frac{1}{2}. The information in bits that you obtain when you learn which symbol has been received (while you know that a “zero” has been transmitted) is ________
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