Download AKTU B-Tech 1st Sem 2016-2017 RAS 104 Professional Communication Question Paper

Code: 13A05305

R13

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

B. Tech II Year I Semester Examinations, November/December - 2016

PROBABILITY AND STATISTICS

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(Common to EEE, ECE, CSE, EIE, ETM)

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 two cards are drawn from a deck of cards what is the probability that both will be diamonds? [2M]

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   2. Define conditional probability. [3M]
   3. A random variable X has density function f(x) = kx², 0 = x = 1, find k. [2M]
   4. Define moment generating function. [3M]
   5. Define critical region. [2M]
   6. Write properties of good estimator. [3M]

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   7. Write the applications of t-distribution. [2M]
   8. Write about Type-I and Type-II errors. [3M]
   9. Define stochastic process. [2M]
   10. Define transient and recurrent state. [3M]

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PART - B (50 Marks)

(Answer all five units, choosing one question from each unit)

UNIT - I

1. 2.a) State and prove Baye’s theorem. [5M]

   b) Two dice are thrown. Find the probability that (i) the sum is greater than 8 and (ii) the sum is neither 7 nor 11. [5M]

   OR

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2. 3.a) A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. What is the probability that the problem is solved? [5M]

   b) If A and B are independent events, prove that A^c and B^c are also independent events. [5M]

UNIT - II

1. 4.a) A continuous random variable has probability density function f(x) given by f(x) = { kx, 0 = x = 2; 2k, 2 = x = 4; -kx + 6k, 4 = x = 6 }. Find k and mean value of X. [5M]

   b) The number of monthly breakdown of a computer is a random variable having a Poisson distribution with mean equal to 1.8. Find the probability that this computer will function without a breakdown during a month. [5M]

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   OR

2. 5.a) Define distribution function and state its properties. [5M]

   b) Out of 800 families with 4 children each, how many families would be expected to have (i) 2 boys and 2 girls (ii) atleast one boy (iii) no girl (iv) atmost two girls. Assume equal probabilities for boys and girls. [5M]

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UNIT - III

1. 6.a) A population consists of 5 numbers 2, 3, 6, 8 and 11. Consider all possible samples of size 2 which can be drawn with replacement from the population. Find [5M]

   1. the mean of the population
   2. the standard deviation of the population
   3. the mean of the sampling distribution of means
   4. the standard deviation of the sampling distribution of means

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   b) State and prove central limit theorem. [5M]

   OR

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

   b) Explain the terms: (i) Null hypothesis (ii) Alternative hypothesis (iii) Critical region (iv) Level of significance. [5M]

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UNIT - IV

1. 8.a) Explain the procedure of testing of hypothesis. [5M]

   b) A random sample of size 16 values from a normal population showed a mean of 53 and a sum of squares of deviations from the mean equals to 150. Can it be regarded as taken from the population having 56 as mean? Obtain 95% confidence limits of the mean of the population. [5M]

   OR

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2. 9.a) Two random samples are drawn from two normal populations are [5M] Sample 1: 20, 16, 26, 27, 23, 22, 18, 24, 25, 19 Sample 2: 27, 33, 42, 35, 32, 34, 38, 28, 41, 43 Test whether the populations have the same variance.

   b) The following are the number of mistakes made in 5 successive days by 4 technicians working for a service department of a company. [5M]

   Technician: A B C D

   Mistakes: 1 3 4 6

   2 4 6 9

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   3 6 5 11

   4 5 7 10

   5 6 8 11

   Test whether the difference among the four technicians is significant.

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UNIT - V

1. 10.a) Define Markov chain. Explain its properties. [5M]

   b) A fair die is tossed repeatedly. If X_n denotes the maximum of the numbers occurring in the first n tosses, find the transition probability matrix P of the Markov chain {X_n}. [5M]

   OR

2. 11.a) Explain queuing model M/M/1: 8 / FIFO. [5M]

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   b) Obtain the steady state probabilities of Markov chain with transition probability matrix P = [ 0 1
   1/2 1/2 ] . [5M]

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