Download AKTU B-Tech 6th Sem 2014-2015 Rural Water Supply and Sanitation Question Paper

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

R18 B.Tech II Year II Semester Examinations, November/December - 2020

PROBABILITY AND STATISTICS

(Common to CSE, IT)

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Time: 3 Hours Max. Marks: 75

Note: This question paper contains two parts A and B.

Part A is compulsory which carries 25 marks. Answer all questions in Part A.

Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks.

PART - A (25 Marks)

1. 1. If P(A) = 1/4, P(B) = 1/3 and P(A n B) = 1/5, then find P(A?B). (2 Marks)

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   2. Define conditional probability. (3 Marks)
   3. Define random variable. (2 Marks)
   4. Write the properties of normal distribution. (3 Marks)
   5. Define population and sample. (2 Marks)
   6. Define Type-I and Type-II errors. (3 Marks)

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   7. Define null and alternative hypothesis. (2 Marks)
   8. Write about control charts. (3 Marks)
   9. What is queuing theory? (2 Marks)
   10. Define Transient and Steady state. (3 Marks)

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PART - B (50 Marks)

(Answer all five units, choosing one question from each unit. Each question carries 10 marks.)

UNIT - I

1. a) A problem in mathematics is given to three students A, B and C. If the probability of A solving the problem is 1/2, B solving the problem is 1/3 and C solving the problem is 1/4, then what is the probability that the problem is solved? [5]
   b) State and prove Baye’s theorem. [5]
   OR

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2. a) A bag contains 5 white and 8 black balls. Two successive drawings of 3 balls are made such that:
   i) Balls are replaced before the second trial ii) Balls are not replaced before the second trial.
   Find the probability that the first drawing will give 3 white and the second 3 black balls. [5]
   b) If X is a continuous random variable whose probability density function is given by f(x) = cx, for 1 = x = 2
   = 0, otherwise
   

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   Find i) the value of c ii) P(1 = X = 1.5). [5]

UNIT - II

1. a) The mean and variance of a binomial distribution are 4 and 4/3 respectively; find P(X = 1). [5]
   b) Fit a Poisson distribution to the following data: [5]
   

   x	0	1	2	3	4
   f	192	100	24	3	1

   
   

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   OR
2. a) If X is a normal variate with mean 30 and standard deviation 5. Find the probabilities that: i) 26 = X = 40, ii) X = 45. [5]
   b) Out of 800 families with 5 children each, how many would you expect to have i) 3 boys ii) at least one boy iii) no girl iv) all girls? Assume equal probabilities for boys and girls. [5]

UNIT - III

1. a) A population consists of the five numbers 2, 3, 6, 8 and 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. [5]
   

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   b) Explain about point estimation and interval estimation. [5]
   OR
2. a) Samples of size 2 are taken from the population 1, 2, 3, 4, 5, 6 with replacement. Find:
   i) The mean of the population ii) The variance of the population
   iii) The mean of the sampling distribution of means iv) The variance of the sampling distribution of means. [5]
   

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   b) Find the maximum error with probability 0.99 while using the mean of a random sample of size n=64 to estimate the mean of a population with variance s² = 16. [5]

UNIT - IV

1. a) The mean life time of 100 bulbs is found to be 1570 hours with standard deviation of 150 hours. Test the hypothesis that the average life time of bulbs is 1600 hours. [5]
   b) Explain the procedure for testing of hypothesis. [5]
   OR

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2. a) The heights of 10 students in a school are 150, 152, 155, 157, 160, 161, 164, 166, 168 and 170 cms. Assuming the heights to be normally distributed, test the hypothesis that the mean height in the school is 160 cms. [5]
   b) Explain about t-test. [5]

UNIT - V

1. a) Explain about M/M/1 queuing model. [5]
   b) Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially with mean 3 minutes.
   

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   i) What is the probability that a person arriving at the booth will find it occupied?
   ii) The telephone company will install a second booth when convinced that an arrival would expect to have to wait at least 3 minutes for the phone. By how much must the flow of arrivals increase in order to justify a second booth? [5]
   OR
2. a) Explain about classification of queuing models. [5]
   b) A super market has two girls serving at the counters. The customers arrive in a Poisson fashion at the rate of 12 per hour. Each girl can serve customers at the rate of 7 per hour. Find: i) What is the probability that a customer has to wait for service? ii) What is the expected percentage of idle time for each girl? [5]

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