JNTU
JNTU B.Tech II PROBABILITY AND STATISTICS Previous Question Paper (December - 2018 - R13)
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.
Part A
(25 Marks)
The probability density function is f(x) = K(3x^2 - 1) for -1 ≤ x ≤ 2, and 0 elsewhere. Find K.
Answer
To find K, we use the condition that the total area under the probability density function must be 1:
Integrating the function:
Thus, K = 1/6.
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. The probability of not drawing a red card is q = 0.5. For n = 6 trials, the probability of getting at least one success is 1 minus the probability of zero successes:
The joint probability density function is f(x, y) = (6-x-y)/8 for 0 < x < 2, 2 < y < 4, and 0 elsewhere. Find the Marginal probability density function for X.
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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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Part B
(50 Marks)
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 3 kgs. 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 X and Y is given by f(x,y). Find f(x) and f(y).
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Calculate the coefficient of rank correlation for the provided X and Y data table.
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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 significant at 0.05 level of significance.
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From the following data find whether there is any significant liking in the habit of taking soft drinks among the categories of employees (Table provided).
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The milk plant at a city distributes its products by trucks. The trucks arrive at the interval of 20 minutes. The service time is 4 minutes. a) What is the probability that there are more than or equal to 4 trucks in the queue? b) What is the waiting time of a truck in the queue? c) 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: a) Average number of problems waiting for the queue. b) The probability that queue length is greater than or equal to five. c) The idle time.
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There are three stores of groceries. A study found initial distribution and monthly transition probabilities. a) What proportion of customers retain by Feb 1st and March 1st b) Find the long run proportions.
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In a presidential election, initial voter registration is provided along with monthly transition probabilities. a) Write transition probability matrix b) Find the % of the voters in each category at the end July.
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