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Some Important Continuous Distributions                         239

           Arkin, H., and Colton, R.1963, Tablesfor Statisticians, 2nd edn., Barnesand Noble, NewYork.
           Beyer, W.H., 1996, Handbook of Tables for Probability and Statistics, Chemical Rubber
            Co., Cleveland, OH.
           Hald, A., 1952, Statistical Tables and Formulas, John Wiley & Sons Inc. New York.
           Owen, D., 1962, Handbook of Statistical Tables, Addision-Wesley, Reading,
           Pearson, E.S., and Harley, H.O. (eds) 1954, Biometrika Tables for Statisticians, Volume 1,
            Cambridge University Press, Cambridge, England.
             Additional useful references include:
           Aitchison,  J.,  and  Brown,  J.A.C.,  1957,  The  Log-normal Distribution,  Cambridge
            University Press, Cambridge, England.
           Harter,  H.L.,  1964, New Tables of the Incomplete Gamma Function Ratio and of Per-
            centage Points of the Chi-square and Beta Distributions, Aerospace Laboratory; US
            Government Printing office, Washington, DC.
           National Bureau  of Standards,  1954,  Tables of the Bivariate Normal Distribution and
            Related Functions: Applied Mathematics Series 50,  US Government  Printing office,
            Washington, DC.


           PROBLEMS

           7.1  The  random  variables  X   and  Y   are  independent  and  uniformly  distributed  in
              interval (0.1). Determine the probability that their product XY  is less than 1/2.
           7.2  The characteristic function (CF) of a random variable X  uniformly distributed in the

              interval ( 1, 1) is
                                             sin t
                                         X …t†ˆ  :
                                               t

              (a)  Find the CF of Y , that is uniformly distributed in interval (  a, a).
              (b)  Find the CF of Y  if it is uniformly distributed in interval (a, a ‡  b).
           7.3 A machine component consisting of a rod-and-sleeve assembly is shown in Figure
              7.15. Owing to machining inaccuracies, the inside diameter of the sleeve is uniformly
              distributed in the interval (1.98 cm, 2.02 cm), and the rod diameter is also uniformly
              distributed in the interval (1.95 cm, 2.00 cm). Assuming independence of these two
              distributions, find the probability that:
              (a) The rod diameter is smaller than the sleeve diameter.
              (b) There is at least a 0.01 cm clearance between the rod and the sleeve.

                                         Sleeve








                                           Rod

                     Figure 7.15 Rod and sleeve arrangement, for Problem 7.3







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