Download AKTU B-Tech 2nd Sem 2014-15 NAS 201 Engineering Physics II Question Paper

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

B.Tech II Year II Semester Examinations, May - 2017

PROBABILITY AND STATISTICS

(Common to ME, CSE, IT, MCT, EIE, MSNT)

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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. Define conditional probability. [2M]

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   2. Write the properties of Binomial distribution. [3M]
   3. Define Null and Alternative hypothesis. [2M]
   4. Explain Type-I and Type-II errors. [3M]
   5. Define population and sample. [2M]
   6. Write the properties of t-distribution. [3M]

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   7. Write about control charts. [2M]
   8. Explain about single and double sampling plans. [3M]
   9. Define Markov chain. [2M]
   10. Write the classification of states. [3M]

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PART - B (50 Marks)

(Answer any one full question from each unit)

UNIT - I

1. a) Two dice are thrown. Let X assign to each outcome (a, b) the larger of the two numbers. Determine the probability distribution of X. Find the mean and variance of the distribution. [5M]

   b) The diameter of an electric cable is assumed to be continuous random variable X with p.d.f f(x) = { 6x(1-x), 0 = x = 1 { 0, otherwise Verify that above is p.d.f and also find the mean and variance. [5M]

   OR

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2. a) Define Poisson distribution and derive its mean and variance. [5M]

   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. [5M]

UNIT - II

1. A population consists of 5 numbers 3, 6, 9, 12, 15. Consider all possible samples of size 2 which can be drawn without replacement from the population. Calculate

   a) The population mean

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   b) The population standard deviation

   c) The mean of the sampling distribution of means

   d) The standard deviation of the sampling distribution of means. [10M]

   OR

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2. a) Find 95% confidence limits for the mean of a normality distributed population from which the following sample was taken 15, 17, 10, 18, 16, 9, 7, 11, 13, 14. [5M]

   b) A random sample of size 100 has a standard deviation of 5. What can you say about the maximum error with 95% confidence? [5M]

UNIT - III

1. a) Explain about tests of hypothesis and types of errors. [5M]

   b) The mean life time of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If µ is the mean lifetime of all the bulbs produced by the company, test the hypothesis µ = 1600 hours, against the alternative hypothesis µ ? 1600 hours, using a 5% level of significance. [5M]

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   OR

2. a) Explain about t-test. [5M]

   b) Two independent samples of sizes 9 and 8 are drawn from two normally distributed populations. The sample means and standard deviations are as follows:

   Sample 1: n₁ = 9, x¯₁ = 196, s₁ = 15

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   Sample 2: n₂ = 8, x¯₂ = 188, s₂ = 18

   Test the hypothesis that µ₁ = µ₂ at 5% level of significance. [5M]

UNIT - IV

1. a) Explain about control charts for variables. [5M]

   b) Construct a control chart for number of defectives. The following data gives the number of defectives in 10 samples, each of size 100. 2, 3, 4, 0, 5, 2, 4, 6, 5, 4. [5M]

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   OR

2. a) Explain about control charts for attributes. [5M]

   b) The following data gives the number of defects in 10 machines. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Draw the relevant control chart. [5M]

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UNIT - V

1. a) Define Stochastic matrix. Explain about transition probabilities. [5M]

   b) The transition probability matrix of a Markov chain is given by P = ? 0.2 0.3 0.5? ? 0.1 0.6 0.3? ? 0.3 0.3 0.4? Find the steady state probabilities of the chain. [5M]

   OR

2. a) Explain about basic queuing process. [5M]

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   b) In a railway yard, goods trains arrive at a rate of 30 trains per day. Assuming that the inter-arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 minutes. Calculate

   i) The mean queue size (line length)

   ii) The probability that the queue size exceeds 10. [5M]

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