GATE EE 2021 Set 1 — Question 8
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67EasyExpectation & VarianceProbabilityEngineering MathematicsPMF, PDF & CDF
Engineering Mathematics → Probability → Expectation & Variance
Last updated
Question
Let be a continuous random variable denoting the temperature measured. The range of temperature is degree Celsius and let the probability density function of be for . The mean of is
Correct answer
(D) 50.0
Solution
The probability density function (PDF) is given as for .
This is the definition of a uniform distribution over the interval , where and .
For a uniform distribution, the PDF is .
In this case, , which matches the given PDF.The mean (expected value) of a continuous random variable with PDF is given by:
For a uniform distribution over , the mean is also given by the formula:
Substituting and :
Thus, the mean of is .The final answer is .
This is the definition of a uniform distribution over the interval , where and .
For a uniform distribution, the PDF is .
In this case, , which matches the given PDF.The mean (expected value) of a continuous random variable with PDF is given by:
For a uniform distribution over , the mean is also given by the formula:
Substituting and :
Thus, the mean of is .The final answer is .
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 EE 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 Probability
2026 Set 1 Q14Consider the following differential equation:…2026 Set 1 Q30Two matrices and have a common eigenvalue , and the same corresponding…2026 Set 1 Q32Given that , the integral…2026 Set 1 Q35 is an skew-symmetric matrix with real-valued entries, and is an…2026 Set 1 Q36A time-limited waveform is specified as follows:…