JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II COMPUTER ORIENTED STATISTICAL METHODS Previous Question Paper (August/September – 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Three machines I, II and III produce 40%, 30% and 30% of the total number of items of a factory. The percentages of defective items of these machines are 4%, 2% and 3%. An item is selected at random and found to be defective. Find the probability that it is from:
i) Machine- I ii) Machine-II iii) Machine-III
Answer
Let A1, A2, and A3 be the events that the item is produced by machines I, II, and III respectively, and let D be the event that the item is defective. The given probabilities are:
P(A1) = 0.40, P(A2) = 0.30, P(A3) = 0.30
P(D|A1) = 0.04, P(D|A2) = 0.02, P(D|A3) = 0.03
The total probability of selecting a defective item is:
Using Bayes' Theorem, the posterior probabilities are:
i) P(A1|D) = (P(A1)P(D|A1)) / P(D) = 0.016 / 0.031 = 16/31 ≈ 0.516
ii) P(A2|D) = (P(A2)P(D|A2)) / P(D) = 0.006 / 0.031 = 6/31 ≈ 0.194
iii) P(A3|D) = (P(A3)P(D|A3)) / P(D) = 0.009 / 0.031 = 9/31 ≈ 0.290
A continuous Random variable has the p.d.f:
Determine: i) P(0 ≤ x ≤ 2) ii) The mean iii) Variance.
Answer
i) P(0 ≤ x ≤ 2) = ∫02 e-x dx = [-e-x]02 = -e-2 - (-e0) = 1 - e-2 ≈ 1 - 0.1353 = 0.8647
ii) The mean (E[X]) is calculated as:
iii) To find the variance, first calculate E[X2]:
Variance (V[X]) = E[X2] - (E[X])2 = 2 - (1)2 = 1
There are three boxes. Box I contains 10 light bulbs (4 defective), Box II contains 6 light bulbs (1 defective), Box III contains 8 light bulbs (3 defective). A box is chosen at random and a bulb is selected. If it is defective find the probability that it is from:
i) Box- I ii) Box-II iii) Box-III
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A continuous Random variable has the p.d.f:
Determine: i) P(2 ≤ x ≤ 4) ii) The mean iii) Variance.
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Six cards are drawn from a pack of 52 cards. Getting a red card is a success. Find the probability of getting the success: i) At least once ii) 3 times
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The probabilities of a Poisson variate taking the values 1 and 2 are equal. Find: i) μ ii) P(x≥1)
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Assume that 60% of the students passed an examination. Find the probability that among 12 students: i) Exactly 8 pass ii) At least 4 pass.
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If the variance of a Poisson variate is 3. Find the probability that: i) P(x=0) ii) P(1 ≤ x < 4).
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In a test on electrical bulbs, it was found that the life was normally distributed with mean 2040 hours and S.D 40 hrs. Estimate the number of bulbs likely to burn for more than 2140 hours.
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Two horses A, B were tested for time to run a track: Horse A: [28, 30, 32, 33, 33, 29, 34]; Horse B: [29, 30, 30, 24, 27, 29]. Test whether the two horses have the same running capacity at 95% level.
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If the masses of 300 students are normally distributed with mean 68 kg and S.D 3 kg. How many students have masses: i) Greater than 72 kg ii) Between 65 and 71 kg.
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The following table gives the number of train accidents during the week. Test whether accidents are uniformly distributed at level 0.05.
| Days | Sun | Mon | Tues | Wed | Thurs | Fri | Sat |
|---|---|---|---|---|---|---|---|
| Accidents | 20 | 18 | 13 | 23 | 26 | 11 | 15 |
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A sample of 900 members has mean 3.4 cm and S.D 2.61 cm. Is this sample taken from a large population of mean 3.25 and S.D 2.61?
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In city A, 20% of 900 school boys had a physical defect. In city B, 18.5% of 1600 school boys had the defect. Is the difference significant at 0.05 level?
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The mobility of population from village, town, and city is given by the transition matrix:
| To Village | To Town | To City | |
|---|---|---|---|
| From Village | 0.3 | 0.2 | 0.5 |
| From Town | 0.3 | 0.5 | 0.2 |
| From City | 0.1 | 0.4 | 0.5 |
Present population is 0.4, 0.3, 0.3 for village, town, and city. Find the proportions after two years and in the long run.
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