JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III PROBABILITY AND STATISTICS Previous Question Paper (February - 2022 - R15)
Answer any five questions
All questions carry equal marks
Main
A random variable X has the pdf
Answer
(i) Since f(x) is a probability density function, the total area under the curve must equal 1:
Integrating the function:
(ii) To find P(X > 1/2):
The first four central moments of a distribution are 0, 2.5, 0.7 and 18.75. Compute β1 and β2.
Answer
Given the central moments: μ1 = 0, μ2 = 2.5, μ3 = 0.7, and μ4 = 18.75.
The coefficient of skewness β1 is defined as:
The coefficient of kurtosis β2 is defined as:
If 30% of items from a factory are defective, find the probability that at least two are defective in a sample of 8.
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Find the moment generating function of Poisson distribution and hence find its mean.
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The joint probability mass function of the random variables X and Y is given by
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From the following data, calculate the correlation coefficient and obtain the two regression lines.
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Y | 9 | 8 | 10 | 12 | 11 | 13 | 14 | 16 | 15 |
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A population consists of the four numbers 1, 5, 6, 8. Consider all possible samples of size 2 that can be drawn without replacement. Find the population mean and standard deviation.
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Find the mean and standard deviation of the sampling distribution of means.
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A manufacturer of electronic equipment subjects two competing brands of transistors to an accelerated performance test. If 45 of 180 transistors of the first kind and 34 of 120 transistors of the second kind fail the test, what can be concluded at the level of significance of 0.05, about the difference between the corresponding sample proportions.
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Derive the formula for the probability distribution density function of the waiting time distribution.
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For a first order stationary random process, show that the mean is constant.
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Show that random process
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