Download AKTU B-Tech 6th Sem 2014-2015 Digital Signal Processing Question Paper

ANURAG GROUP OF INSTITUTIONS

Autonomous

II B.Tech I Semester Regular Examinations Nov/Dec 2023

PROBABILITY AND STATISTICS

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(CSE, CSE(AI&ML), CSE(DS), CSE(CS))

Time: 3 Hours Max. Marks: 70

Note: Answer all questions from Part A and Part B. Assume missing data, if any, suitably

PART – A (10 x 2 = 20 Marks)

1. a) Define Random Variable.
2. b) Write the formula for variance of Binomial Distribution.

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3. c) Define Null Hypothesis.
4. d) Write type-I and type-II errors.
5. e) Define Transient state and Steady state.
6. f) Define Kendall’s notation.
7. g) Define Regression.

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8. h) Write the formula for Spearman’s Rank Correlation.
9. i) What is meant by statistical quality control?
10. j) Define control charts.

PART – B (5 x 10 = 50 Marks)

11. a) If the probability density of a random variable is given by f(x) = kx², 0 = x = 1, find i) the value of k ii) P(0.2 = x = 0.5) (OR)

b) In a Normal distribution, 7% of the items are under 35 and 89% are under 63. Determine the mean and variance of the distribution.

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12. a) A population consists of five numbers 2, 3, 6, 8, 11. Consider all possible samples of size 2 which can be drawn with replacement from this population. Find i) The mean of the population ii) The standard deviation of the population iii) The mean of the sampling distribution of means iv) The standard deviation of the sampling distribution of means (OR)

b) Explain the procedure for testing of hypothesis.

13. a) Assume that both the number of customer arrivals and the service times are exponentially distributed. The average arrival rate is 12 per hour and the average service time is 4 minutes. What are the average number of customers in the system and the average time a customer spends in the system? (OR)

b) A fast-food restaurant has one drive-in window. It is estimated that cars arrive according to a Poisson distribution at the rate of 2 every 5 minutes and that there is enough space to accommodate a line of 10 cars. Other arriving cars can wait outside this space, if necessary. Assume that a car is served on a FIFO basis and it takes 1.5 minutes on the average to serve a customer. Find i) The probability that the drive-in window is idle ii) The average number of customers waiting to be served

14. a) Calculate the coefficient of correlation and obtain the lines of regression for the following data:

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(OR)

b) From the following data, find: i) The two regression equations ii) The coefficient of correlation between the marks in Economics and Statistics iii) The most likely marks in Statistics when marks in Economics are 30.

15. a) Construct a control chart for the number of defects from the following data.

(OR)

b) What are the advantages of statistical quality control?

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