www.studentyogi.com                                                            www.studentyogi.com
       Code No: ECM2221...
www.studentyogi.com                                                           www.studentyogi.com
       Code No: ECM2221
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E C M2221 P R O B A B I L I T Y A N D S T A T I S T I C S Set1


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E C M2221 P R O B A B I L I T Y A N D S T A T I S T I C S Set1

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E C M2221 P R O B A B I L I T Y A N D S T A T I S T I C S Set1

  1. 1. www.studentyogi.com www.studentyogi.com Code No: ECM2221 RA III B.Tech I Semester Regular Examinations, November 2008 PROBABILITY AND STATISTICS (Electronics & Computer Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks 1. (a) For any three arbitrary events A, B, C , prove that P (A B C) = P (A) + P (B) + P (C) - P (A n B) - P (B n C) - P (C n A) + P (A n B n C ) (b) In a certain town 40% have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. A person is select at random from the town i. If he has brown hair, what is the probability that he has brown eyes also ii. If he has brown eyes, determine the probability that he does not have brown hair [8+8] 2. (a) Probability density function of a random variable X = 1/2 sin x in 0 = x = p = 0 else where. Find the mean, mode and median for the distribution and also nd the prob- ability between 0 and p 2 (b) Two dice one thrown 5 times. If getting a double of is a success. Find the probability that getting the success i. atleast once ii. Two times. [8+8] 3. (a) If a Poisson distribution is such that P(x=1). 3 2 = P(x=3). Find i. p(x =1) ii. p(x = 3) iii. p(2= x = 5) (b) A sales tax o cer has reported that the average sales of the 500 business that he has to deal with during a year is Rs.36,000 with a standard deviation of 10,000. Assuming that the sales in these business are normally distributed, nd i. the number of business as the sales of while are Rs.40,000/- ii. the percentage of business the sales of while are likely to range between Rs. 30,000/- and Rs.40,000/- [8+8] 4. (a) What is the probability that X will be between 75 and 78 if a random sample of size 100 taken from an in nite population has mean 76 and variance 256. 1 of 2 www.studentyogi.com www.studentyogi.com
  2. 2. www.studentyogi.com www.studentyogi.com Code No: ECM2221 RA (b) According to the norms established for a mechanical aptitude test persons who are 18 years old should average 73.2 with a standard deviation 8.6. If 4 randomly selected persons of that age averaged 76.7, test the null hypoth- esis µ = 73.2 against the alternate hypothesis µ > 73.2 at the 0.01 level of signi cance? [8+8] 5. (a) In a study of an automobile insurance a random sample of 80 body repair costs had a mean of Rs. 472.36 and a standard deviation of Rs 62.35. If x is used as a point estimate to the true average repair costs, with what con dence we can assert that the maximum error doesn’t exceed Rs. 10? (b) A manufacturer of electric bulbs claims that the percentage defectives in his product doesn’t exceed 6. A sample of 40 bulbs is found to contain 5 defectives. Would you consider the claim justi ed? [8+8] 6. A pair of dice are thrown 360 times and the frequency of each sum is indicated below: Sum 2 3 4 5 6 7 8 9 10 11 12 Frequency 8 24 35 37 44 65 51 42 26 14 14 Would you say that the dice are fair on the basis of the chi-square test at .05 level of signi cance. [16] 7. Fit an equation of the form Y=abx to the following data: x: 2 3 4 5 6 y: 144 172.8 248.8 298.5 298.5 [16] 8. (a) If there are no ties in the ranks then show that the rank correlation is given be = 1 - 6Sd2 i n(n2 -1) where di = rank of xi rank of yi (b) For 20 army personnel, the regression of weight of kidneys (y) on weight of heart (x), both measured in oz, is y = 0.399 x + 6.394 and the regression of weight of heart on weight of kidneys is x = 1.212y - 2.461. Find the correlation coe cient between the two variables and also their means. [8+8] 2 of 2 www.studentyogi.com www.studentyogi.com