B.TechSemester 52023-24Statistical ComputingKIT051
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Statistical Computing (KIT051) - AKTU Question Paper 2023-24

B.Tech · Semester 5 · Free PDF Download

This is the official AKTU Statistical Computing Previous Year Question Paper for B.Tech Semester 5, academic session 2023-24. Published by Dr. A.P.J. Abdul Kalam Technical University (AKTU/UPTU), Lucknow. Free PDF download — no login required.

Course:B.Tech
Semester:Semester 5
Session:2023-24
University:AKTU / UPTU

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Questions Asked in 2023-24

Statistical Computing (KIT051) — complete question paper · 100 marks · 3 Hours

Section AAttempt all q u e s t i o n s i n b r i e f .
  • a
    Discuss the significance of measures of dispersion in a dataset . Provide examples of two measures of dispersion and explain how they differ
  • b
    Define the concept of "mean" as a measure of central tendency. How is it calculated, and what are its advantages and limitations?
  • c
    Explain the concept of correlation and its significance in stat istical analysis. Provide an example of a positive and a negative correlation
  • d
    Outline the steps involved in conducting an inference procedure for a correlation coefficient. Why is it important in statistical analysis?
  • e
    Differentiate between bivariate correlation and simple correlat ion. Provide an example scenario where bivariate correlation would be more appropriate
  • f
    Explain the concept of linear regression. How is the regression line determined, and what does the slope of the line represent in a regression analysis?
  • g
    Describe the key differences between simple linear regression a nd multiple regression. Why might a researcher choose to use multiple regression?
  • h
    Compute the correlation coeffici ent for the following paired da ta: X (hours of study) - 10, 15, 20, 25; Y (exam scores) - 60, 75, 80, 90. i. Given the dataset: X - 2, 4, 6, 8; Y - 5, 8, 11, 14, find the equation of the regression line (Y on X). j. In a deck of 52 cards, what is the probability of drawing a queen given that the card drawn is a face card?
Section BAttempt any three o f t h e f o l l o w i n g :
  • a
    Apply singular value decomposition (SVD) to a given matrix B. D iscuss the significance of the singular values and how they contribute to linear dimension reduction
  • b
    Conduct a multiple regression analysis using a dataset with two independent variables. Interpret the coefficients and assess the overall fit of the model
  • c
    In a study comparing two teaching methods, Group A has 15 students taught with Method 1, and Group B has 20 students taught with Method 2. The exam scores for both groups are given. Use a randomization test to determin e i f t h e r e i s a significant difference in the mean scores between the two groups
  • d
    (i) Define principal component analysis (PCA) and its purpose in linear dimension reduction. Discuss the steps involved in PCA. (ii) Apply PCA to a dataset with five variables. Interpret the results and explain how PCA aids in dimensionality reduction
  • e
    A random sample of 50 students is selected from a population. The average hours of study per week for the sample is 15 hours, with a standard deviation of 3 hours. Calculate a 95% confidence interval for the mean hours of study for the population
Section CAttempt any one p a r t o f t h e f o l l o w i n g :
  • a
    Perform a Monte Carlo simulation to test the hypothesis that th e mean of a population is 50, based on a sample of 30 observations with a k nown standard deviation of 10. Use 1000 simulated samples and a significance level of 0.05
  • b
    Define Markov chains and explain their role in Markov Chain Mon te Carlo (McMC) methods. Discuss the importance of convergence in McMC simulations
  • a
    Explain how Monte Carlo simulations can be used for hypothesis testing. Discuss the advantages of Monte Carlo hypothesis testing over traditional methods
  • b
    Explain the concept of the jackknife resampling method. Apply t he jackknife to estimate the variance of the mean for a dataset with 30 observations
  • a
    Perform a permutation test to compare the means of two independ ent groups (Group A: 25 observations, Group B: 30 observations). The observed difference in means is 2.5, and the permutation distribution yields differences of -1.8, -0.5, 1.0
  • b
    Use the jackknife resampling method to estimate the bias and variance of the mean for a dataset with 40 observations. Present the jackknife-estimated mean, bias, and variance
  • a
    Perform 5-fold cross-validation on a linear regression model. T he dataset has 80 observations, and the mean squared error for each fold is as fo llows: 12, 15, 10, 18, 14. Compute the average mean squared error across the folds
  • b
    Briefly discuss the history and origin of the R programming lan guage. Highlight key milestones and contributors
  • a
    Save a vector of numbers (e.g., c(2, 4, 6, 8, 10)) to the R wor kspace. Show how to inspect the variables in the workspace and display their values
  • b
    Define a vector with the elements 1 to 5. Create a matrix with 3 rows and 2 columns using the vector. Display both the vector and the matrix

Question text is extracted from the official AKTU question paper PDF above. Hindi translations are omitted — every question is printed in English in the original paper. Last verified: 2026-08-23.

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