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Previous year question hub

Estimation - Statistics Previous Year Questions

Practice Estimation - Statistics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

8Papers
8Years
49Questions
1Topics

Estimation question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Estimation. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 27 55.1%
Hard 12 24.5%
Easy 10 20.4%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 30 61.2%
Numerical Answer Type (NAT) 15 30.6%
MSQ 4 8.2%

Subject weightage

Top subjects by unique question coverage.

Statistics
49 Qs

Most asked topics

Top topics across the included previous year papers.

Estimation
49 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Moment and Maximum-likelihood Estimation
17 Qs
Unbiased Estimation and Variance Bounds
14 Qs
Sufficiency, Completeness and Ancillarity
12 Qs
Interval estimation
6 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Statistics (ST) 2026
7 Qs
Statistics (ST) 2025
6 Qs
Statistics (ST) 2024
4 Qs
Statistics (ST) 2023
6 Qs
Statistics (ST) 2022
8 Qs
Statistics (ST) 2021
5 Qs
Statistics (ST) 2020
6 Qs
Statistics (ST) 2019
7 Qs

Browse by subtopics

Open a focused page built from the same verified paper data.

Moment and Maximum-likelihood Estimation

Explore previous-paper coverage, trends and focused practice for Moment and Maximum-likelihood Estimation.

17 questions8 papers8 years

Unbiased Estimation and Variance Bounds

Explore previous-paper coverage, trends and focused practice for Unbiased Estimation and Variance Bounds.

14 questions7 papers7 years

Sufficiency, Completeness and Ancillarity

Explore previous-paper coverage, trends and focused practice for Sufficiency, Completeness and Ancillarity.

12 questions6 papers6 years

Interval estimation

Explore previous-paper coverage, trends and focused practice for Interval estimation.

6 questions5 papers5 years

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Statistics (ST) 202620267View paper
Statistics (ST) 202520256View paper
Statistics (ST) 202420244View paper
Statistics (ST) 202320236View paper
Statistics (ST) 202220228View paper
Statistics (ST) 202120215View paper
Statistics (ST) 202020206View paper
Statistics (ST) 201920197View paper

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
2019 · Statistics · Estimation · Moment and Maximum-likelihood Estimation
Statistics (ST) 2019
Let \(X_1, ..., X_n\) be a random sample drawn from a population with probability density function \(f(x; \theta) = \theta x^{\theta-1}, 0 \le x \le 1, \theta > 0\). Then the maximum likelihood estimator of \(\theta\) is
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2
2020 · Statistics · Estimation · Interval estimation
Statistics (ST) 2020
Let \(X_1, \ldots, X_{10}\) be a random sample from a Weibull distribution with the probability density function \(f(x; \theta) = \begin{cases} 3\theta x^2 e^{-\theta x^3}, & x > 0 \\ 0, & \text{otherwise} \end{cases}\) where \(\theta \in (0, \infty)\). For any positive integer \(v\) and any \(\alpha \in (0, 1)\), let \(\chi^2_{v, \alpha}\) denote the \((1 - \alpha)\)-th quantile of the central chi-square distribution with \(v\) degrees of freedom. Then, a 90% confidence interval for \(\theta\) is
Open complete paper
3
2021 · Statistics · Estimation · Moment and Maximum-likelihood Estimation
Statistics (ST) 2021
Let \(X_1, X_2, \ldots, X_n\) be a random sample of size \(n\) (≥ 2) from a distribution having the probability density function \[f(x; \theta) = \begin{cases} \frac{1}{\theta} e^{-\frac{x-\theta}{\theta}}, & x > \theta, \\ 0, & \text{otherwise}, \end{cases}\] where \(\theta \in (0, \infty)\). Then the method of moments estimator of \(\theta\) equals
Open complete paper
4
2022 · Statistics · Estimation · Unbiased Estimation and Variance Bounds
Statistics (ST) 2022
Let \(S^2\) be the variance of a random sample of size \(n > 1\) from a normal population with an unknown mean \(\mu\) and an unknown finite variance \(\sigma^2 > 0\). Consider the following statements:
(I) \(S^2\) is an unbiased estimator of \(\sigma^2\), and \(S\) is an unbiased estimator of \(\sigma\).
(II) \(\left(\frac{n-1}{n}\right)S^2\) is a maximum likelihood estimator of \(\sigma^2\), and \(\sqrt{\frac{n-1}{n}} S\) is a maximum likelihood estimator of \(\sigma\).
Which of the above statements is/are true?
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5
2023 · Statistics · Estimation · Moment and Maximum-likelihood Estimation
Statistics (ST) 2023
Let \( X \) be a random variable with probability density function
\( f(x; \lambda) = \begin{cases} \frac{1}{\lambda} e^{-\frac{x}{\lambda}} & \text{if } x > 0 \\ 0 & \text{otherwise}, \end{cases} \)
where \( \lambda > 0 \) is an unknown parameter. Let \( Y_1, Y_2, \ldots, Y_n \) be a random sample of size \( n \) from a population having the same distribution as \( X^2 \).
If \( \bar{Y} = \frac{1}{n} \sum_{i=1}^n Y_i \), then which one of the following statements is true?
Open complete paper
6
2024 · Statistics · Estimation · Sufficiency, Completeness and Ancillarity
Statistics (ST) 2024
Let \( X_1, X_2, X_3 \) be three independent and identically distributed binomial random variables with number of trials \( n = 100 \) and success probability \( p \) (0 < p < 1), which is an unknown parameter. Let \( T_1 = (X_1 + X_2, X_3) \) and \( T_2 = X_1 + X_2 + X_3 \). Consider the following statements:
(I) The distribution of \( T_2 \) given \( T_1 = t_1 \) is independent of \( p \).
(II) The distribution of \( T_1 \) given \( T_2 = t_2 \) is independent of \( p \).
Which of the above statements is/are true?
Open complete paper