GATE EC 2023 Set 1 — Question 36
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67HardFunctions of Random VariablesProbabilityEngineering Mathematics
Engineering Mathematics → Probability → Functions of Random Variables
Last updated
Question
A random variable , distributed normally as , undergoes the transformation , given in the figure. The form of the probability density function of is
(In the options given below, are non-zero constants and is piece-wise continuous function)
(In the options given below, are non-zero constants and is piece-wise continuous function)
Correct answer
(B) aδ(y + 1) + bδ(y) + cδ(y - 1) + g(y)
Solution
The transformation has constant segments at (for ), (for ), and (for ). For a continuous random variable , any region where the transformation function is constant results in a discrete probability mass at that value in the distribution of , which manifests as an impulse in the PDF. Therefore, the PDF will have impulses at , , and . The general form is , where represents the continuous part of the PDF corresponding to the non-constant regions of . This matches option (B).
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 Probability
2026 Set 1 Q11Consider the differential equation , with…2026 Set 1 Q12A surface is given by and and are unit…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…2026 Set 1 Q36Consider the two series, and , where …