JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II COMPUTATIONAL STATISTICS 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.
PART – A
State division algorithm.
Answer
The division algorithm states that for any two integers a and b, where b > 0, there exist unique integers q (the quotient) and r (the remainder) such that:
Mention any two examples for linear congruences.
Answer
A linear congruence is a congruence of the form ax ≡ b (mod m). Two examples are:
- 3x ≡ 6 (mod 9): Here, a=3, b=6, and m=9. Since gcd(3, 9) = 3 and 3 divides 6, this congruence has three distinct solutions: x ≡ 2, 5, 8 (mod 9).
- 5x ≡ 3 (mod 7): Here, a=5, b=3, and m=7. Since gcd(5, 7) = 1, this congruence has a unique solution. Multiplying by the modular multiplicative inverse of 5 modulo 7 (which is 3), we get x ≡ 9 ≡ 2 (mod 7).
Define two-way ANOVA.
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Mention any suitable example for multiple correlation.
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Mention the probability density function of the normal distribution.
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Define central limit theorem.
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Mention any suitable example of the standard error.
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Give any suitable example for type-2 error.
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Define transient state.
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Write any two examples for Absorbing state.
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PART – B
Prove that for any integer a, one of the integers a, a+2, a+4 is divisible by 3.
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Prove that if gcd(a, b) = 1, then gcd(a+ b, ab)= 1.
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Compute the correlation coefficient between the corresponding values of X and Y in the following table:
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A random variable X has the following probability function:
Find k
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P(X < 6)
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P(0 < X < 5)
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The mean yield for one-acre plot is 662 kilos with a standard deviation 32 kilos. Assuming normal distribution, how many one-acre plots in a batch of 1000 plots would you expect to have yield (a) over 700 kilos (b) below 650 kilos (c) between 630 kilos and 690 kilos.
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The average number of articles produced by two machines per day is 200 and 250 with standard deviation 20 and 25 respectively on the basis of records of 25 days of production. Can you regard both the machines as equally efficient at 1% level of significance?
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In a sample survey of 1000 housewives in a city, 23 percent preferred a particular brand of pressure cooker. Find 99 percent confidence limits for percentage of all housewives in the city preferring that brand of cooker.
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A quality control expert is required to estimate the mean thickness of aluminum sheets used in the production of airframes. A sample of 100 sheets reveals a mean of 0.048 inches with a standard deviation of 0.01 inches. Construct 99 percent confidence interval.
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The mean height of 50 male students who showed above-average participation in college athletics was 68.2 inches with a standard deviation of 2.5 inches, while 50 male students who showed no interest in such population had a mean height of 67.5 inches with a standard deviation of 2.8 inches. Test that male students who participate in college athletics are taller than other male students.
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In a three-state Markov chain with state E1, E2, E3, the chain starts in E2 so that P(0) = [0 1 0]. Find the absolute probability P(3), if the transition matrix is:
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A four-state Markov chain has the transition matrix:
Draw transition diagram
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show that E1 is a transient state.
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