UPSC Statistics 2021

(a) A production unit manufacturing surgical masks is concerned about the quality of their masks. A random sample of n masks are inspected to estimate 'p', the probability of manu…

(a) Let Y₁, Y₂, Y₃, ... be independent and identical Poisson random variables with parameter 1. Use central limit theorem to establish n! ≃ √(2π n)(n/e)ⁿ for large value of positi…

(a) Let X and Y be two independent random variables following exponential distribution with mean 1/(λ) and 1/(μ) respectively, λ > 0, μ > 0. Suppose that (X₁, X₂, ..., Xₙ) and (Y₁…

(a) Let X₁, X₂, ..., Xₙ be a random sample from Poisson distribution with mean λ > 0. Define a statistic W = (1 − 1/n)^T, T = Σᵢ₌₁ⁿ Xᵢ (i) Show that T is complete sufficient stati…

(a) For a simple linear regression model Y = β₀ + β₁Xᵢ + εᵢ, i = 1, ..., n (i) Derive the least square estimators of β₀ and β₁, clearly stating the conditions assumed. (ii) For eᵢ…

(a) For a multiple linear regression model with three covariates X₁, X₂ and X₃, let rᵢⱼ denote the correlation coefficient between Xᵢ and Xⱼ. For a data, it was found r₁₂ = 0·77,…

(a) (i) What is confounding in factorial experiments ? (ii) A 2^6factorial experiment is conducted in blocks of size2³. Write the confounded effects such that no main effect or tw…

(a) (i) In stratified sampling under optimum allocation, how will you proceed to select units from different strata, if one or more nᵢ's happens to be greater than Nᵢ (i ≥ 2) ? (i…

Explain Single Sampling Plan with the help of an example. Also, write the importance of an Operating Characteristics Curve in a sampling plan. (10 marks) Solve the above assignmen…

A manufacturer finds that on the average, a television set is used 1.8 hours per day. A one year warranty is offered on the picture tube having a mean time to failure (MTTF) of 20…

(a) Explain M|G|1 queuing system. Obtain Pollaczek-kinchine formula. (15 marks) (b) Use MODI method to solve the above transportation problem: Store I II III IV A 4 6 8 13 B 13 11…

(a) Solve the following linear programming problem: Maximize z = 3x₁ + 5x₂ subject to the constraints 3x₁ + 2x₂ ≤ 18 x₁ ≤ 4 x₂ ≤ 6 and x₁, x₂ ≥ 0. Discuss the change in Cⱼ on the…

(a) Explain Zellner's seemingly unrelated regression model and the feasible generalized least squares method of estimating the model. (10 marks) (b) Explain the functions of N.S.S…

(a) Explain Box-Jenkins methodology to build ARIMA models. (15 marks) (b) Prepare the cost of living index for 2006 on the basis of 2005 from the above data by (i) aggregative met…

(a) If c(x, t) denote observed proportion of females in the age group (x, x+t) and f(x, t) is the observed proportion of females giving birth to female children in the age group (…

(a) What is autocorrelation ? What are its consequences ? Explain the Goldfeld-Quandt test and Glesjer test for heteroscedasticity. (20 marks) (b) Check the identifiability of the…