GATE EC 2014 Set 1 — Question 62
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumInformation Measure & EntropyInformation TheoryCommunicationsRandom VariablesProbabilityEngineering Mathematics
Communications → Information Theory → Information Measure & Entropy
Last updated
Question
A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let be the number of tosses to get this first ‘Head’. The entropy
H(L) in bits is ________.Correct answer
1.99 to 2.01
Solution
The random variable represents the number of trials until the first success (Head) in a sequence of independent Bernoulli trials with probability of success . This follows a geometric distribution.The probability mass function (PMF) of is given by:The entropy
H(L) in bits is defined as:This is an arithmetico-geometric series. The sum of the series for is given by .Substituting :Thus, the entropy H(L) is 2 bits.Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Information Theory
2026 Set 1 Q11Consider the differential equation , with…2026 Set 1 Q12A surface is given by and and are unit…2026 Set 1 Q22Consider a discrete memoryless source with an alphabet of four source symbols. is a…2026 Set 1 Q23The relation between the input current () and the output voltage () of a circuit is governed…2026 Set 1 Q26Consider the matrix . Which…