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Posted By: kondapalli Member Level: Gold Posted Date: 07 May 2008
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2007 Jawaharlal Nehru Technological University B.Tech Computer Science & Engineering PROBABILITY AND STATISTICS setno3 Question paper
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1. (a) Two aero planes bomb a target in succession. The probability of each correctly
scoring a hit is 0.3 and 0.2 respectively. The second will bomb only if the first
misses the target. Find the probability that
i. one target is hit
ii. both fails to score hits
(b) There are three boxes. Box I contains 10 light bulbs of which 4 are defective.
Box II contains 6 light bulbs of which one is defective. Box III contains 8 light
bulbs of which 3 are defective. A box is chosen and a bulb is drawn. Find the
probability that the bulb is non defective. [8+8]
2. (a) If f(x) = K e-1x1 is a probability density function in -1< x <1, find
i. The value of k,
ii. the variance
iii. The probability between 0 and 4.
(b) Derive the mean and variance of the Binomial distribution. [8+8]
3. (a) If x is a Poisson variate such that 3p (x = 4) = 1
2p (x = 2) + p (x = 0) find
i. the mean of x
ii. p(x2)
(b) Prove that the mean = mode = median for a normal distribution. [8+8]
4. A population consists of 5,10,14,18,13,24 consider all possible samples of size two
which can be drawn without replacement from the population. Find
(a) The mean of the population.
(b) The standard deviation of the population.
(c) The mean of the sampling distribution of means
(d) The standard deviation of sampling distribution of means. [4X4]
5. (a) A random sample of size 100 has a standard deviation of 5. What can you say
about the maximum error with 95% confidence.
(b) Among 900 people in a state 90 are found to be chapatti eaters. Construct
99% confidence interval for the true proportion.
(c) A random sample of 1200 apples was taken from a large consignment and
found that 10% of them are bad. The supplier claims that only 2% are bad.
Test his claim at 95% level. [5+5+6]
6. Two independent samples of sound 7 items respectively had the following values.
Sample I 11 11 13 11 15 9 12 14
Sample II 9 11 10 13 9 8 10 -
In the difference between the means of samples significant? [16]
7. (a) Derive normal equations to fit the parabola y = a0 + a1x + a2x
2
(b) Fit the parabola y = a0 + a1x + a2x
2 for the following data [6+10]
X 0 1 2 3 4
Y 1 1.8 1.3 2.5 6.3
8. The following data relate to the marks of 10 students in the internal test and the
university examination for the maximum of 50 each
Internal marks (x) 25 28 30 32 35 36 38 39 42 45
University marks (y) 20 26 29 30 25 18 26 35 35 46
Find the coefficient of correlation and the two lines of regression. [16]
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