JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD MCA 2019 PROBABILITY AND STATISTICS Previous Question Paper (April/May - 2019 - R09)
Answer any five questions
All questions carry equal marks
Main
Define Probability. Find the probability of getting 2 diamonds, if we draw 2 cards at random from a pack of 52 cards.
Answer
Probability is a numerical measure of the likelihood that a specific event will occur, defined as the ratio of the number of favorable outcomes to the total number of equally likely possible outcomes in a sample space.
To find the probability of drawing 2 diamonds from a pack of 52 cards:
- Total number of ways to draw 2 cards from 52 is 52C2 = (52 × 51) / (2 × 1) = 1326.
- Number of diamonds in a pack is 13. The number of ways to draw 2 diamonds from 13 is 13C2 = (13 × 12) / (2 × 1) = 78.
- The probability P = 78 / 1326 = 1 / 17.
An integer is chosen at random from the first 200 positive integers. What is the Probability that the integer chosen is divisible by 6 or 8
Answer
Let S be the set of the first 200 positive integers, so n(S) = 200. Let A be the set of integers divisible by 6 and B be the set of integers divisible by 8.
- The number of integers divisible by 6 is n(A) = floor(200 / 6) = 33.
- The number of integers divisible by 8 is n(B) = floor(200 / 8) = 25.
- The intersection A ∩ B consists of integers divisible by the least common multiple of 6 and 8, which is 24. Thus, n(A ∩ B) = floor(200 / 24) = 8.
- Using the addition theorem of probability, n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 33 + 25 - 8 = 50.
- The required probability is P(A ∪ B) = n(A ∪ B) / n(S) = 50 / 200 = 1 / 4 or 0.25.
Explain Conditional Probability. If the Probability that a communication system will have high fidelity is 0.81 and the Probability that it will have high fidelity and selectivity is 0.18. What is the Probability that a system with high fidelity will also have high selectivity?
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State and Prove Baye’s Theorem
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Find the mean and variance of the Binomial Distribution
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Four coins are tossed 160 times. The number of times x heads occur (x = 0, 1, 2, 3, 4) is given below. Fit the Binomial distribution
| x | 0 | 1 | 2 | 3 | 4 |
| No.of times | 8 | 34 | 69 | 43 | 6 |
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Show that the Mean and Variance of Poisson distribution are equal
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If X is a poisson variate such that P(X=0) = P(X=1) find P(X=0) and Using recurrence formula find the probabilities at x = 1, 2, 3, 4 and 5.
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Derive the mean and median of Normal Distribution
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1000 students had written an examination the mean of test is 35 and Standard deviation is 5. Assuming the distribution to be normal find How many students marks lie between 25 and 40?
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A sample of 100 electric light bulbs produced by a manufacturer A showed a mean lifetime of 1190hrs. and a standard deviation of 90hrs. A sample of 75 bulbs, produced by a manufacturer B showed a mean life time of 1230 hrs with a S.D of 120 hrs. Is there difference between the mean life times of the two brands at a significant level of 0.05?
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Explain Bayesian estimation.
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Two independent samples of 8 and 7 items respectively had the following values of the variables
| Sample I | 9 | 11 | 13 | 11 | 16 | 10 | 12 | 14 |
| Sample II | 11 | 13 | 11 | 14 | 10 | 8 | 10 | - |
Do the estimates of population variances differ significantly?
A random sample of size 100 is taken from an infinite population having the mean μ = 76 and the variance σ2 = 256. What is the probability that x will be between 75 and 78
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Compute the coefficient of correlation and the two lines of regression for the following data
| x | 14 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| y | 84 | 78 | 70 | 75 | 66 | 67 | 62 | 58 | 60 |
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