Success TrackerSuccess Tracker
Log inSign up

GATE EE 2023 Set 1 — Question 25

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
MCQ+1 / -0.33MediumExpectation & VarianceProbabilityEngineering MathematicsNormal DistributionStatistics & DistributionsSampling Theorems

Engineering Mathematics → Probability → Expectation & Variance

Last updated

Question

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation σo\sigma_o. The σo\sigma_o is estimated by randomly drawing out 10,000 numbers of samples (xnx_n). The estimates σ^1,σ^2\hat{\sigma}_1, \hat{\sigma}_2 are computed in the following two ways.σ^12=110000∑n=110000xn2σ^22=19999∑n=110000xn2\hat{\sigma}_1^2 = \frac{1}{10000} \sum_{n=1}^{10000} x_n^2 \quad \hat{\sigma}_2^2 = \frac{1}{9999} \sum_{n=1}^{10000} x_n^2Which of the following statements is true?
Your answer

Choose one option, then check your answer.

The solution stays hidden until you check.

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.

Start with a free accountView plans and allowances

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 n×nn \times n matrices AA and BB have a common eigenvalue 22, and the same corresponding…2026 Set 1 Q32Given that F⃗(x,y,z)=sin⁡(y)x^+cos⁡(x)y^+5z^\vec{F}(x, y, z) = \sin(y) \hat{x} + \cos(x) \hat{y} + 5 \hat{z}, the integral…2026 Set 1 Q35AA is an m×mm \times m skew-symmetric matrix with real-valued entries, and xx is an…2026 Set 1 Q36A time-limited waveform g(x)g(x) is specified as follows:…