JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II PROBABILITY AND STATISTICS Previous Question Paper (December - 2018 - R15)
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 and may have a, b, c as sub questions.
Main
The probability density function is
Answer
For a valid probability density function, the integral over the entire range must equal 1. Given the function f(x) = k(1-x^2), we solve:
Integrating gives k[x - x^3/3] from 0 to 1, resulting in k(1 - 1/3) = 1, which simplifies to 2k/3 = 1. Thus, k = 1.5.
Six cards are drawn from a pack of 52 cards. Getting a red card is a success. Find the probability of getting the success at least once.
Answer
The probability of drawing a red card in a single draw is p = 26/52 = 0.5. For 6 cards, the number of red cards X follows a binomial distribution B(6, 0.5). The probability of at least one success is 1 - P(X=0).
Therefore, P(X ≥ 1) = 1 - 1/64 = 63/64 ≈ 0.9844.
The joint probability density function is given by
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The equations of two Regression lines are y=11.64-0.5x, x=19.13-0.87y, find the Coefficient of Correlation.
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Define tail I and tail II tests.
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A Random sample of 1500 items is taken from a population whose standard deviation is 45. Find the maximum error.
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Define Waiting time and Mean arrival rate.
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What are the assumptions for the postulates for the poisson process?
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Define an irreducible Marcov chain.
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What are the properties of a transition matrix?
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A die is thrown 8 times. If getting 2 or 4 is a success, find the probability of getting: i) 4 successes. ii) P( x ≤ 3) (x being the number of failures)
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Suppose that the weights of 800 male students are normally distributed with mean μ = 140 pounds with a standard deviation of 10 pounds. Find the number of students whose weight are: i) Between 138 and 148 ii) More than 152.
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If the variance of a Poisson variate is 2, find the probability that: i) x =0 ii) 1< x < 4.
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If the masses of 300 students are normally distributed with mean 68 kgs and standard deviation 3kgs. How many students have masses i) Greater than 72 kgs ii) Between 65 and 71 kgs.
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The joint probability density function of the continuous random variables and is given by. Find f(x), f(y).
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Calculate the coefficient of rank correlation for the given data.
| x | 68 | 64 | 75 | 50 | 64 | 80 | 75 | 40 | 55 | 64 |
| y | 62 | 58 | 68 | 45 | 81 | 60 | 68 | 48 | 50 | 70 |
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In a city A 20% of a random sample of 900 school boys had a certain slight physical defect. In another city B 18.5% of a random sample of 1600 school boys had the same defect. Is the difference between the proportions is significant at 0.05 level of significance.
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From the following data find whether there is any significant liking in the habbit of taking soft drinks among the categories of employees.
| Soft drinks | clerks | teachers | officers |
|---|---|---|---|
| Pepsi | 10 | 25 | 65 |
| Thumps up | 15 | 30 | 65 |
| Sprite | 50 | 60 | 30 |
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The milk plant at a city distributes its products by trucks, loaded at the loading dock. It was its own fleet of trucks plus trucks of a private transport company. The trucks arrive at the interval of 20 minutes. The service time is 4 minutes.
What is the probability that there are more than or equal to 4 trucks in the queue?
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What is the waiting time of a truck in the queue?
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What is the variance of queue length?
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Problems arrive at a computer centre in Poisson fashion with a mean arrival rate of 25 per hour. The average computing job requires 2 minutes of terminal time. Calculate the following:
Average number of problems waiting for the queue.
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The probability that queue length is greater than or equal to five.
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The idle time.
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There are three stores of groceries. There will be a shift from one to another. A study was made in January first and it was found that 1/4 was shopped at store1, 1/3 at 2 and 5/12 at 3. Every month store1 retain 90% of their customers and 10% transformed to store2. Store2 retain 5% of their customers and 85% transformed to store1 and store3. Store3 retain 40% of their customers and 50% transformed to store1 and 10% to store2.
What proportion of customers retain by Feb 1st and March 1st
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Find the long run proportions.
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In a presidential election at the end f June 40% of the voters registered for liberal, 45% for conservative and 15% for independent. Over one month, of the people those who registered for liberal 80% were retained, 15% changed to conservative and 5% to independent. Of the people those who registered for conservative 70% were retained, 20% changed to liberal and 10% to independent. Of the people those who registered for independent, 60% were retained, 20% changed to liberal and 20% to conservative.
Write transition probability matrix
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Find the % of the voters in each category at the end July
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