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II B.Tech I Semester Regular Examinations, December 2017/January 2018
PROBABILITY AND STATISTICS
(Common to Civil Engineering, Mechanical Engineering and Information Technology)
Time: 3 hours Max. Marks: 70
Note: 1. Question Paper consists of two parts (Part-A and Part-B)
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2. Answer ALL the question in Part-A
3. Answer any THREE Questions from Part-B
PART-A
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1. a) Define Random variable and Mathematical expectation. [4M]
b) Find the Moment generating function of Poisson distribution. [4M]
c) Define Null and Alternative hypothesis. [4M]
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d) Write about types of errors in sampling. [4M]
e) Write properties of Queuing system. [3M]
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f) Define Markov chain. [3M]
PART-B
2. a) The probability density function is given by
$$f(x) = \begin{cases}
Kx^2, & 0 \le x \le 2 \\
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0, & \text{otherwise}\end{cases}$$
Find K and P(1<x<2). [8M]
b) Find the Moment generating function of Normal distribution. [8M]
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3. a) A population consists of five numbers 2,3,6,8,11. Consider all possible samples of size 2 which can be drawn without replacement from the population. Find
i) The mean of the population
ii) The standard deviation of the population
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iii) The mean of the sampling distribution of means
iv) The standard deviation of the sampling distribution of means. [8M]
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b) Explain about point estimation and interval estimation. [8M]
4. a) A sample of 26 bulbs gives a mean life of 990 hours with a S.D of 20 hours. The manufacturer claims that the average life of bulbs is 1000 hours. Is the sample not up to the standard. [8M]
b) Two independent samples of sizes 9 and 7 from a normal population gave the following values.
Sample1: 18 13 12 15 12 14 16 14 15
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Sample2: 16 21 15 16 14 18 13Is the difference between the means significant? [8M]
5. a) If there are 24 calls are coming to the telephone exchange in one hour. Find the probability of
i) There will be 3 or less calls to the exchange in one hour
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ii) There are 5 calls in 12 minutes. [8M]
b) In a railway yard, goods trains arrive at the rate of 30 trains per day. Assuming that the inter arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 minutes. Calculate the following:
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i) The mean queue size
ii) The probability that the queue size exceeds 10 [8M]
6. a) The transition probability matrix is given by
$$P = \begin{bmatrix}
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0.1 & 0.5 & 0.4 \\0.6 & 0.2 & 0.2 \\
0.3 & 0.4 & 0.3
\end{bmatrix}$$
Is the Markov chain is ergodic? Explain. [8M]
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b) Three states 0, 1, 2, the transition probability matrix is
$$P = \begin{bmatrix}
0 & 1 & 0 \\
0.5 & 0 & 0.5 \\
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0 & 1 & 0\end{bmatrix}$$
Find the stationary probabilities. [8M]
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This download link is referred from the post: VNSGU MBBS Last 15 Years 2010-2025 Previous Question Papers (Veer Narmad South Gujarat University)
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