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.. -- ::>- ...Register Number:Nameof the Candidate:

3 100D.E. DEGREE EXAMINATION, 2009

(CIVIL, STRUCTURAL, MECHANICAL,MANUFACTURING ENGINEERING)

(FOURTH SEMESTER)CLEC I CSEC IMEEC I MFEC -401.PROBABILITY AND STATISTICS

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(b) An urn -A contains 3 white balls and I5 black balls. Another urn - B contains \5 white balls and 3 black balls. Two,balls are transferred from A to Bandthen one ball is drawn from B. What is ithe probability that it is block? . 'I

2. (a) The first four central moments of adistribution are 0, 3, 0 and 26. Themean of tbe variable is 5. Calculate thefirst fo~r moments a~out the value zero.

(b) If two dice are thrown, what is theprobability that the sum is

(i) Greater than 8.(ii) Neither 7 nor 1I.

UNIT- II3. (a) A random variable X has the following

probability function:

3(i) Determine the value of a.(ii) Find:

P(x

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4UNIT -III

5. (a) Find the binomial distribution for whichthe mean is 4 and variance is 3.

(b) Define uniform distribution. Find its meanand variance.6. (a) If X is a Poisson variate

P(X = 2) = 9 P(X = 4) + 90 P(X = 6),find mean and variance of X.

(b) If X is normally distributed and the meanof X is 12 and the S.D is 4. find outthe probability of the following:

(i) X ::: 20.(ii) X ~ 20.(iii) 0 ~ X ~ 12.

UNIT - IV7. (a)

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(b) Nine items of a sample had the followingvalues:45 47, 50, 52, 48, 47, 49, 53 and 51..'Doe~ the mean of the nine items differsignificantly from the assumed populationmean 47.5.

8. (a) A random sample of 500 pineapples wastaken from a large consignment and 65were found to be bad. Find thepercentage of bad pineapples in theconsignment.

(b) Two horses A and B were testedaccording to the time (in seconds) to runa particular trade with the followingresults:

Test whether the two horses have the

Horse -A : 28 30 32 33 33 29 34Horse - B : 29 30 30 24 27 29 -

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6UNIT -V

9. (a) The design of a component with mean:ilife equal to 10 hours is modified to'

improve its mean life to 20 hours. Whatis the increase in its reliability if inboth cases the component is tested fOf'20 hours?

(b) Five elements (a, b, c, d .and j) of' asystem are connected as shown in thefollowing figure, which also indicates thereliability of each element. Calculate thesystem reliability.

ca

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10. (a) Explain, what are areas, where reliabilityand MTBF can be good use.(b) A product with a constant hazard rate isfound to have a reliability of 80 % for an

operating time of 500 hours. What is thefailure rate of the product?