A question from this chapter

Question 1

2026 PYQ

For a given data set {x_{1}, x_{2}, \dots ., x_{n}}, where n = 100, it is known that \frac{1}{2000} i = 1 \sum n j = 1 \sum n (x_{i} - x_{j})^{2} = 99 Let us denote \overset{x}{ˉ} = \frac{1}{n} \sum_{i = 1}^{n} x_{i} The value of \frac{1}{99} i = 1 \sum n (x_{i} - \overset{x}{ˉ})^{2} is __________ . (Answer in integer)

Question 2

2026 PYQ

Let X_{1}, X_{2}, \dots ., X_{n} be n independent random variables. Each of the random variables follows N or ma l (μ = 0, σ^{2} = 1) distribution. Define \overset{ˉ}{X} = \frac{1}{n} \sum_{i = 1}^{n} X_{i} . Which of the following statements is/are correct?

Statistical Inference PYQs for GATE DA

GATE DA Statistical Inference: 2 chapters, 4 previous year questions (11% of Probability and Statistics), 0 practice questions and one solved question from each chapter.

About Statistical Inference Previous Year Questions (PYQs)

4 previous year questions from Statistical Inference in GATE DA, grouped by chapter with the exam year, answer key and step-by-step solution for each.

Statistical Inference Weightage in GATE DA

Statistical Inference accounts for 4 of 35 Probability and Statistics previous year questions in our bank (11%), about 1.3 per paper across 3 papers.

Statistical Inference Chapter Matrix

Chapter	Topics	PYQs	Share of unit PYQs	Practice questions
Sample Mean, Variance and Descriptive Estimation	Sample Mean Updates and Sample Variance Identities	2	50%	0
Sampling Distributions and Estimator Properties	Sampling Distributions and Chi-Square Results, Estimator Bias and Variance Properties	2	50%	0

One Solved Question from Each Statistical Inference Chapter

Question 1 · Sample Mean, Variance and Descriptive Estimation · 2026 NAT

For a given data set

{x_{1}, x_{2}, \dots ., x_{n}}

, where

n = 100

, it is known that

\frac{1}{2000} i = 1 \sum n j = 1 \sum n (x_{i} - x_{j})^{2} = 99

Let us denote

\overset{x}{ˉ} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}

The value of

\frac{1}{99} i = 1 \sum n (x_{i} - \overset{x}{ˉ})^{2}

is __________ . (Answer in integer)

Question 2 · Sampling Distributions and Estimator Properties · 2026 MSQ

Let

X_{1}, X_{2}, \dots ., X_{n}

n

independent random variables. Each of the random variables follows

N or ma l (μ = 0, σ^{2} = 1)

distribution. Define

\overset{ˉ}{X} = \frac{1}{n} \sum_{i = 1}^{n} X_{i}

.

Which of the following statements is/are correct?

A.
$\sum_{i = 1}^{n} X_{i}^{2}$ follows Chi-square distribution with $n$ degrees of freedom.
B.
$\sum_{i = 1}^{n} (X_{i} - \overset{ˉ}{X})^{2}$ follows Chi-square distribution with $(n - 1)$ degrees of freedom.
C.
$X_{1}^{2} + X_{n}^{2}$ follows exponential distribution with mean 2.
D.
$(n \overset{ˉ}{X})^{2}$ follows Chi-square distribution with 2 degrees of freedom.

A question from this chapter

Login to view the complete previous-year questions and solutions

Personalised first. High quality throughout.

Built around you, not around a syllabus PDF

Revision that hits your weak spots

Questions calibrated to the real exam

Notes written for recall, not for volume

One place for everything

Honest progress

Unlock the whole course

Statistical Inference PYQs for GATE DA

About Statistical Inference Previous Year Questions (PYQs)

Statistical Inference Weightage in GATE DA

Statistical Inference Chapter Matrix

More from Probability and Statistics

One Solved Question from Each Statistical Inference Chapter