Mathematics-IV Unit 4 – Statistical Techniques II: AKTU previous year questions
50 AKTU questions from Unit 4 (Statistical Techniques II) asked in 2021–2026, tagged by marks, year and topic. In short: about 30 marks of every paper come from this unit; the most asked topic is Probability and Random Variables (20 times); 11 questions came back in a later year. The latest ones are listed below; on the page you can filter them by 2-mark or long questions, topic and repeats.
Unit 4 previous year questions
- Define a probability density function (p.d.f.) and state its two properties. (2 marks, 2026, Probability and Random Variables)
- The lifetime of an electric bulb is normally distributed with mean 1200 hours and standard deviation 100 hours. 1. Find the probability that a bulb lasts (a) more than 1300 hours, (b) between 1100 and 1250 hours. 2. Out of 2000 bulbs, how many are expected to last more than 1400 hours? (7 marks, 2026, Normal Distribution)
- The number of typing errors per page in a book follows a Poisson distribution with mean 2. 1. Find the probability that a randomly chosen page has (a) no error (b) at most two errors. 2. If a book has 500 pages, estimate the expected number of pages with exactly three errors. (7 marks, 2026, Poisson Distribution)
- A discrete random variable X has the following probability distribution: x: 0 1 2 3 4, P(X=x): k 2k 3k 2k k. Find the value of k and determine the mean and variance of X. (7 marks, 2026, Probability and Random Variables)
- Find p and q of Binomial distribution whose mean is 9 and variance 9/4. (2 marks, 2025, Binomial Distribution)
- Explain the probability density function. (2 marks, 2025, Probability and Random Variables)
- If X and Y are two random variables having joint density function: f(x,y) = (1/8)(6-x-y); 0 ≤ x < 2, 2 ≤ y < 4; 0 otherwise. Find P(X < 1 ∩ Y < 3). (2 marks, 2025, Probability and Random Variables)
- If the heights of 300 students are normally distributed with mean 64.5 inches and standard deviation 3.3 inches, find the height below which 99% of the students lie (P(z=2.327)=0.49). (7 marks, 2025, Normal Distribution)
- If Z is a standard normal variable, find the following probabilities: (i) P(Z < 1.2) (ii) P(Z > -1.2) (iii) P(-1.2 < Z < 1.3). (7 marks, 2025, Normal Distribution)
- In a certain factory turning out razor blades, there is a small chance of 0.002 for any blade to be defective. The blades are supplied in packets of 10. Calculate the approx. no. of packets containing (i) no defective (ii) one defective (iii) two defective blades in a consignment of 10,000 packets. (7 marks, 2025, Poisson Distribution)
- A manufacturer knows that the condensers he makes contain on an average 1% of defectives. He packs them in boxes of 100. What is the probability that a box picked at random will contain 4 or more faulty condensers? (7 marks, 2025, Poisson Distribution)
- A die is tossed thrice. A success is getting 1 or 6 on a toss. Find the mean and variance of the number of successes. (7 marks, 2025, Binomial Distribution)
Most asked Unit 4 topics
- Probability and Random Variables – asked 20 times
- Normal Distribution – asked 11 times
- Binomial Distribution – asked 10 times
Unit 4 question pattern
- 2-mark questions: 19 asked in 2021–2026
- 7-mark questions: 15 asked in 2021–2026
- 10-mark questions: 16 asked in 2021–2026
- About 30 marks from Unit 4 in every paper
- 11 questions were asked again in a later year
Unit 4 questions year by year
- 2026: 4 Unit 4 questions asked (23 marks across that year's papers)
- 2025: 9 Unit 4 questions asked (48 marks across that year's papers)
- 2024: 11 Unit 4 questions asked (52 marks across that year's papers)
- 2023: 10 Unit 4 questions asked (68 marks across that year's papers)
- 2022: 10 Unit 4 questions asked (68 marks across that year's papers)
- 2021: 6 Unit 4 questions asked (44 marks across that year's papers)