Download JNTUH MCA 1st Year R19 2021 July-August 861AD Computer Oriented Statistical Methods Question Paper

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R19

Code No: 861AD

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, July/August - 2021

COMPUTER ORIENTED STATISTICAL METHODS

Time: 3 Hours Max. Marks: 75

Answer any five questions

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All questions carry equal marks

1. 1. In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively, are defective. What is the probability that a randomly selected finished product is defective?
   2. You enter a chess tournament where your probability of winning a game is 0.3 against half the players 0.4 against a quarter of the players and 0.5 against the remaining quarter of the players you play a game against a randomly chosen opponent. What is the probability of winning? [8+7]
2. 1. A random variable X may assume 4 values with probabilities. Find the condition on x so that these values represent the probability function of X.

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   2. The joint probability density function of two random variables X and Y is
      Find : 1) the marginal density of X and Y ii) Are X and Y are independent? [7+8]
3. 1. Find the mean of the random variable whose probability density function is given by flx)=3/510° (100—x) 0< x < 100.
   2. If X is the number appearing on a die when it is thrown, show that the Chebshev’s theorem given P[ | X | >2.5]<0.47, while the actual probability is zero. [8+7]

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4. 1. Show that mean = variance for a Poisson distribution.
   2. Probability of a success is given by 0.4 if n = §, find the 1) P(x>/) 11) P(0<x<4) . [7+8]
5. 1. The lognormal distribution is found to be a good model for strains in structural members caused by wind loads. Let the strain be represented by X, with my = 1 and variance of X is 0.09. (1) Determine the probability P(X > 1 2). (ii) If stress Y in a structural member is related to the strain by Y =a+ bX, with b > 0, determine f y (y) and my .

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   2. The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated independently, are being erected at the same time, what is the probability that at least 2 will still stand after 35 years? [8+7]
6. 1. Take 30 slips of paper and lable 5 each -4 and +4, lable 4 from each -3 and 3, three each -2 and 2 and two each -1, 0, and 1. If each slip of paper has the same probability of being drawn, find the probabilities of getting -4,-3,-2,-1,0,1,2,3,4 and find the mean and the variance of this distribution.
   2. Find the probabilities that a random variable having the standard normal distribution will take on a value 1) Between 0.87 and 1.28 ii) between -0.34 and 0.62. [7+8]

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7. 1. A manufacturer of electric lamps is testing a new production method that will be considered acceptable if the lamps produced by this method result in a normal population with an average life of 2,400 hours and a standard deviation equal to 300. A sample of 100 lamps produced by this method has an average life of 2,320 hours. Can the hypothesis of validity for the new manufacturing process be accepted with a risk equal to or less than 5%?
   2. Among 200 items 50 are defective and from another sample among 400 items 80 are defective. Test at 0.05 level whether there is a significant difference between the proportions. [8+7]
8. 1. Find the linear least square fity = a x + b for the experimental data points given by: {1,2),(3,4).,(2,6),4.8),(5,12),(6,13),(7,15)}
   2. The following regressions equations were obtained from a correction table y=0.516x +33.73 x=0.512y +32.52
      

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      Find the value of 1) The correlation coefficient ii) The mean x’s iii) the mean of y’s. [7+8]

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