Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II Year STATISTICAL METHODS FOR DATA SCIENCE Previous Question Paper (April/May - 2023 - R18)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions. iv) Table values for test statistics are to be provided to the students
Part A
Define CV and State its use.
Answer
The Coefficient of Variation (CV) is a relative measure of dispersion defined as the ratio of the standard deviation to the mean, expressed as a percentage. It is calculated as:
Its primary use is to compare the variability or consistency of two or more data sets, even if they are measured in different units or have significantly different means.
List the Axioms of Probability.
Answer
The three fundamental axioms of probability for any events A and B in a sample space S are:
- Non-negativity: The probability of any event is non-negative: P(A) ≥ 0.
- Normalization: The probability of the entire sample space is 1: P(S) = 1.
- Additivity: For any sequence of mutually exclusive events A1, A2, ..., the probability of their union is the sum of their individual probabilities: P(∪ Aᵢ) = Σ P(Aᵢ).
Define discrete and continuous random variables.
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A random variable x has the following probability function: values of x: -2, -1, 0, 1, 2, 3, and respective p(x): 0.1, k, 0.2, 2k, 0.3, k. Find the value of k and calculate mean.
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What is Critical Region?
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Mention the applications of Normal Distribution.
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How to test the goodness of fit?
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State the properties of F-distribution.
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What is the use of scatter diagram?
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What do you understand by Logistic Regression?
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Part B
If P(A) = 0.3, P(B) = 0.2, P(A ∪ B) = 0.4 find P(A ∩ B). Examine whether A and B are independent.
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Explain about moment measures with suitable examples.
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Discuss the different measures of central tendency of a frequency distribution, mentioning their merits and demerits.
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A box contains 3 blue and 2 red balls while another box contains 2 blue and 5 red balls. A ball drawn at random from one of the boxes turns out to be blue. What is the probability that it came from the first box?
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Suppose that the random variables X and Y have a joint density function given by. Find: a) the constant c, b) the marginal density functions for X and Y, c) P(3 < X < 4, Y > 2), d) P(X > 3), e) P(X + Y > 4), f) Whether X and Y are independent.
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Let X and Y be random variables having joint density function. Find i) E(X), ii) E(Y), iii) E(X + Y), iv) E(XY).
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Show that the function is a probability density function.
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Two dice are thrown five times find the probability of getting 7 as sum i) Atleast once ii) Exactly two times.
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The following data given for two samples: Sample I (Mean 65, S.D. 2, Size 400), Sample II (Mean 63, S.D. 1, Size 100). Construct 95% confidence interval for μ1 – μ2.
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A random sample of size 144 is taken from an infinite population having the mean 75 and variance 225. What is the probability that sample mean will be between 72 and 77.
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In a sample of 500 students 15 use ball pens, and among 800 of another sample 80 use ball pens. Construct large sample 99% confidence interval for the true difference of two proportions.
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To compare the prices of a certain product in two cities ten shops were selected at random in each town. The prices are: City I (61, 62, 56, 63, 56, 63, 58, 56, 44, 61), City II (55, 54, 47, 59, 51, 61, 57, 54, 64, 58). Test whether the average prices can be said to be same in the two cities.
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Five coins are tossed 320 times the number of heads 0, 1, 2, 3, 4, 5 are observed with the frequencies 15, 45, 85, 95, 60, 20 respectively. Examine whether the coin is unbiased.
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A random sample of 10 bags of pesticides are taken whose weights are 50, 49, 52, 44, 45, 48, 46, 45, 49, 45 (in kgs). Test whether the average packing can be taken to be 50 Kgs.
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The time taken by workers in performing a job by methods I and II is: Method I (20, 16, 26, 27, 23, 22), Method II (27, 33, 42, 35, 32, 34, 38). Do the data show that the variances of time distribution from population from which these samples are drawn do not differ significantly?
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Find the least squares regression equation of X1 on X2 and X3 from the following data:
| X1 | 3 | 5 | 6 | 8 | 12 | 14 |
|---|---|---|---|---|---|---|
| X2 | 16 | 10 | 7 | 4 | 3 | 2 |
| X3 | 90 | 72 | 54 | 42 | 30 | 12 |
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Discuss about Correlation and Regression.
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Find the rank correlation coefficient between marks in two subjects A and B scored by 10 students: A(88, 72, 95, 60, 35, 46, 52, 58, 30, 67), B(65, 90, 86, 72, 30, 54, 38, 43, 48, 75).
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