Download JNTUH MCA 1st Year R19 2022 May 861AD Computer Oriented Statistical Methods Question Paper

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Code No: 861AD R19

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA I Semester Examinations, May - 2022

COMPUTER ORIENTED STATISTICAL METHODS

Time: 3 Hours Max.Marks:75

Answer any five questions

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All questions carry equal marks

1. a) In a bolt factory machines A, B, C manufacture 20%, 30% and 50% of the total of their output and 6%, 3% and 2% are defective. A bolt is drawn at random and found to be defective. Find the probabilities that it is manufactured form (1) Machine A (i1) Machine B (ii1) Machine C.
2. b) The daily consumption of electric power (in millions of kw-hours) is a random variable having the probability density function f(x)=xe^-x, x>0 0, x<0 If the total production is 12 million kw-hours, determine the probability that there is power cut (shortage) on any given day. [5+10]
3. a) A random variable x has the following probability distribution.
   X=x 1 2 3 4 5 6 7 8
   

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   P(X = x) k 2k 3k 4k 5k 6k 7k 8k
   Find the value of
   Dk 1) p(x=2) i) p(2 <x < 5).
4. b) Find the constant K such that f(x) = { Kx², 0< x<3 0, otherwise is probability density function. Also find mean of X. [5+10]
5. a) If two cards are drawn from a pack of 52 cards which are diamonds, using Poisson distribution, find the probability of getting two diamonds at least 3 times in 51 consecutive trials of two cards drawing each time.

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6. b) Out of 800 families with 5 children each, how many would you expect to have 1) 3 boys i1) 5 girls iii) either 2 or 3 boys? Assume equal probabilities for boys and girls.
7. a) If X is a Poisson Variate such that 3p(x =4) = %p(x =2)+p(x =0), find
   i)mean of x 1) p(x < 2) [5+6+4]
8. b) Fit a Poisson distribution to the following data:
   X 0 1 2 3 4 5 6 7
   

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   f 305 365 210 80 28 9 2 1
9. The probability that an entering student will graduate is 0.4. Determine the probability that out of 5 students 1) one will graduate ii) at least one will graduate. [10+5]

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1. a) Prove that mean, median and mode of a Normal distribution are equal.
2. b) If X is a normal variate with mean 30 and standard deviation 5. Find the probabilities that 1) 26 < x < 40 ii) x > 45. [10+5]
3. a) Population consists of five numbers 2,3, 6, 8 and 11. Consider all possible samples with replacement from this population.
   Find
   1) The mean of population
   

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   i1) The standard deviation of population.
   i1i1) The mean of sampling distribution of means.
   1v) The standard deviation of sampling distribution of means.
4. b) A sample of size 300 was taken whose variance is 225 and mean 54. Construct 95% confidence interval limits for the mean p. [9+6]
5. a) Write a short notes on Type-I and Type-II errors

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6. b) A random sample of size 81 was taken whose variance is 20.25 and mean is 32. Find the maximum error and construct 98% confidence interval.
7. A sample of size 300 was taken whose variance is 225 and mean 54. Construct 95% confidence interval limits for the mean p. [5+5+5]
8. The two regression equations of the variables{x and y are x = 19.13 — 0.87y and y = 11.64 — 0.50x find i) mean of x's ii) mean of y’s iii) correlation coefficient between x and y
9. Calculate the regression equations of y on”x from the data given below, taking deviations from actual mean of x and y
   x 10 12 13 12 16 15
   

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   y 40 38 43 45 37 43
   Estimate the value of y when x = 20. [7+8]

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