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ENSH 301Bachelor in Agriculture Engineering · Semester 54 Papers Available

Probability and Statistics

Past examination question papers and complete curriculum syllabus for Probability and Statistics (ENSH 301), Bachelor in Agriculture Engineering Semester 5 under Institute of Engineering (IOE), Tribhuvan University.

Sem 5 Subjects (4)View Full Semester Overview →
ENCE 301Irrigation and Drainage EngineeringENAG 302Farm Power and TractorsENCE 302Engineering HydrologyENSH 301Probability and Statistics
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5th-sem_Probability and Statistics.pdf

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Most Frequently Asked Questions

Top recurring IOE board exam questions for Probability and Statistics with verified mark schemes, formula notation, and recurrence frequency.

Showing 40 of 40 top repeated questions
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Year-wise & Session-wise Exam Papers

Complete questions from each exam session (Regular & Back exams from 2082 to 2069) for Probability and Statistics. Click any session paper to expand.

Showing 311 questions across 19 exam session papers
Institute of Engineering • 2083 Baishakh Board Examination
Q1[2 Marks]Descriptive Statistics and Basic Probability
Define conditional probability and addition law of probability. There are three machines A, B and C producing 3000, 4000 and 5000 bulbs respectively. These machines are known to be producing 1%, 2% and 3% defectives respectively. One bulb is selected at random and it was found to be defective. What is the probability that the bulb is produced from: (a) Machine A (b) Machine B
Q2[5 Marks]Probability Distributions and Sampling Distribution
A certain type of ball is manufactured with a mean strength of 7.83 kilogram and standard deviation of 0.56 kilogram. Find the probability that a random sample of 16 balls will have average strength. (a) Less than 8 kilograms (b) Between 8 and 9 kilograms
Q3[5 Marks]Probability Distributions and Sampling Distribution
From the population of size as: and . a) List out all the samples of size three without replacement. b) Find the sample proportion of even number. c) Prove that, sample proportion is unbiased estimator proportion of even number. . d) Also find the standard error of sample proportion of even number.
Q4[5 Marks]Statistical Inference
A recent survey claims that of adults prefer reading news online rather than from printed newspapers. A researcher believes this proportion has changed. To test this claim, a random sample of adults is selected, and of them say they prefer reading news online. Using a level of significance, test whether the proportion of adults who prefer reading news online has changed from .
Q5[8 Marks]Statistical Inference
Over a period of days the percentage relative humidity in a vegetable storage building was measured. Mean daily values were recorded as shown below: a) Find the sample mean. (b) Find sample standard deviation. (c) Estimate confidence interval for true mean daily relative humidity from these data.
Q6[5 Marks]Correlation and Regression
If a researcher what to apply ANOVA analysis in his research, what steps should he/she follows?
Q7[5 Marks]Probability Distributions and Sampling Distribution
What are the differences and similarities between Binomial and Negative Binomial Distribution?
Q8[5 Marks]Statistical Quality Control
A quality control engineers inspects a random sample of 3 batteries from each lot of 24 car batteries that is ready to shipment. If such a lot contain six batteries with slight defects, what is the probabilities that the inspector's sample will contain a) None of the batteries with defect b) Only one of the batteries with defect c) At least two of the batteries with defect
Q9[5 Marks]Probability Distributions and Sampling Distribution
A continuous random variable X has probability density function defined as follows. (i) Find the value of constant k. (ii) Mean and the distribution function of X.
Q10[8 Marks]Probability Distributions and Sampling Distribution
Define central limit theorem for sampling distribution of mean and discuss its importance in Inferential statistics. The life time of a certain brand of electric bulb may be considered a random variable with mean hours and standard deviation hours. Find the probability that the average lifetime of sample of bulbs: (i) Exceed hours (ii) Is between hours and hours.
Q11[5 Marks]Descriptive Statistics and Basic Probability
Define the correlation coefficient and mention its important properties. What does the coefficient of determination measure?

Curriculum Syllabus & Course Topics

Sourced from TU curriculum portal
Full Syllabus (PDF)
Chapter-wise Units & Micro-Syllabus Topics (5 Units)

  1. 1. Descriptive Statistics and Basic Probability

    • 1.1Introduction to statistics and its importance in engineering
    • 1.2Measure of central tendency and measure of variation
    • 1.3Graphical representation of data: Histograms, box plots and scatter plots
    • 1.4Basic probability concepts, additive law, multiplicative law
    • 1.5Conditional probability and Bayes’ theorem

  2. 2. Probability Distributions and Sampling Distribution

    • 2.1Random variables: Discrete and continuous
    • 2.2Expectation and variance of discrete and continuous random variables
    • 2.3Discrete probability distributions: Binomial, Poisson, negative Binomial
    • 2.4Continuous probability distributions: Normal, Gamma, Chi-Square
    • 2.5Population and sample
    • 2.6Sampling distribution of mean and proportion
    • 2.7Central limit theorem

  3. 3. Statistical Inference

    • 3.1Point estimations and properties of estimators
    • 3.2Confidence intervals for mean and proportions
    • 3.3Hypothesis testing, parametric and non-parametric tests, procedure of hypothesis
    • 3.4Hypothesis testing of mean (Single mean, two means, paired t-test and one-way)
    • 3.5Goodness of fit tests and independence of attributes (Chi-square and Kolmogorov–Smirnov test)

  4. 4. Correlation and Regression

    • 4.1Correlation analysis and test of linear correlation
    • 4.2Simple regression analysis, the concept of explained, unexplained, and total
    • 4.3Multiple regression analysis

  5. 5. Statistical Quality Control

    • 5.1Quality control and its importance in engineering
    • 5.2Control charts for variables (X-bar, R-chart, P-chat)
    • 5.3Six sigma concepts

Examination Scheme & Marks Distribution

Evaluation Structure

  • Final Board Theory Exam: 60 Marks (Pass mark: 24)
  • Internal Assessment: 40 Marks (Pass mark: 16)
  • Practical / Lab Exam: 25 or 50 Marks (Continuous lab evaluation + viva, where applicable)

* This is the general current IOE 60/40 scheme; verify course-specific details in the syllabus above.

Exam Preparation Guidelines

  • Review the 4 available past examination papers to identify recurring patterns, core problem types, and chapter weightage.
  • Practice numerical problems step-by-step with clean formula derivations, clear units, and standard assumptions.
  • Structure answers with labeled diagrams, concise bullet points, and highlight final answers in numerical solutions.
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Curriculum Syllabus & Marking Scheme