Bibliography. Problems in Probability Downloaded from by on 04/12/18. For personal use only.

Transcription

1 Bibliography 1. Adams, W., The Life and Times of the Central Limit Theorem, New York: Kaedmon Publishing Co., Kolmogorov in Perspective, Providence: American Mathematical Society, Andrews, G., Askey, R. and Roy, R., Special Functions, Cambridge: Cambridge University Press, Apostol, T., Mathematical Analysis, Reading, Mass.: Addison-Wesley, Artin, E., The Gamma Function, New York: Holt, Rinehart and Winston, Australia. Office of the Australian Actuary, Australian Life Tables, , Canberra: Australian Government Publishing Service, Bennett, D.J. Randomness, Cambridge, Mass: Harvard University Press. 8. Bharucha-Reid, A.T. and Sambandham, M., Random Polynomials. Orlando: Academic Press, Box, G.E.P. and Muller, M.E., A note on the generation of random normal deviates. Annales of Mathematical Statistics, v. 29 (1958), pp Breiman, L., Probability, Philadelphia: Society for Industrial and Applied Mathematics, Butzer, P. and Jongmans, F., P. L. Chebyshev ( ). A guide to his life and work. J. Approx. Theory, v.96, no. 1 (1999), pp Chatfield, C. The Analysis of Time Series: An Introduction, 5th ed. London: Chapman and Hall, (no author) Pafnutiĭ Lvovich Chebyshev (on the 175th anniversary of his birth), Theory Probab. Appl., v. 41, no. 3 (1996), pp Chebyshev, P.L. et al., Oeuvres de P.L. Tchebychef, vols. 1 and 2, New York: Chelsea, Clark, R., Tattslotto numbers and the perception of randomness. Research Report 251, Department of Mathematics, Monash University, Clark, R., Are your Tattslotto numbers overdue? Research Report 255, Department of Mathematics, Monash University,

2 176 Bibliography 17.Copi, I.M., Symbolic Logic, 5th ed., New York: Macmillan, Courant, R., Differential and Integral Calculus, Vol. I, 2nd ed., London: Blackie & Sons, Cox, D. and Miller, H., The Theory of Stochastic Processes, London: Chapman and Hall. 20.Cramér, H., Mathematical Methods of Statistics, Princeton: Princeton University Press, Doob, J.L., Measure Theory, New York: Springer-Verlag, Durrett, R., Probability Theory and Examples, Pacific Grove: Wadsworth, Epstein, R.A., The Theory of Gambling and Statistical Logic, New York: Academic Press, Erdős, P. and Révész, P., Problems and results on random walks. In Mathematical Statistics and Probability Theory, Vol. B (Bad Tatzmannsdorf, 1986) ed. P. Bauer et al., Dordrecht-Boston, MA-London: Reidel, 1987, pp Feller, W., Introduction to Probability Theory and Its Applications, vol. 1, 3rd ed. New York: John Wiley & Sons, Freund, J.E. and Perles, B.M., Statistics: A First Course, 7th. ed. Upper Saddle River: Prentice Hall, Grimmett, G.R. and Stirzaker, D.R., Probability and Random Processes: Problems and Solutions, Oxford: OUP, Hald, A., Statistical Theory of Sampling Inspection by Attributes, London: Academic Press, Halmos, P., Measure Theory, Princeton: D. van Nostrand, Hammersley, J.M. and Handscomb, D.C., Monte Carlo Methods, London: Methuen, Harward, P.M. and Mills, T.M. (1980) How to invert a matrix and probably get the right answer. Menemui Mathematik, vol. 2, no.1 pp Henze, N. and Riedwyl, H., How To Win More: Strategies for Increasing a Lottery Win, Natick, Mass: A.K. Peters, Heyde, C.C., Patrick Alfred Pierce Moran Available URL: 34.Heyde, C.C. and Seneta, E., Statisticians of the Centuries. New York: Springer-Verlag, Jacod, J. and Protter, P., Probability Essentials. Berlin: Springer-Verlag, Jones, B., Barry Jones Dictionary of Biography. Melbourne: Information Australia, Kahaner, D., Moler, C., and Nash, S., Numerical Methods and Software, Englewood Cliffs: Prentice Hall, Kendall, M.G. and Moran, P.A.P., Geometric Probability, London: Griffin, Keyfitz, N. and Beekman, J.A. Demography Through Problems, New York: Springer-Verlag, 1984.

3 Bibliography Kolmogorov, A.N., Foundations of the Theory of Probability, 2nd English Edition. New York: Chelsea, Krige, D.G., Statistical applications in mine valuation. J. Institute Mine Surveyors of South Africa, vol. 12, no. 2/3 (1962), pp Lukacs, E., Characteristic Functions, Second Edition, London: Griffin, Maor, E., e: The Story of a Number, Princeton: Princeton University Press, Mitra, A., Quality Control and Improvement, Second Edition, Upper Saddle River: Prentice-Hall, Moran, P., An Introduction to Probability Theory, Oxford: OUP, Moran, P.A.P., Calculation of the normal distribution function. Biometrika, vol. 67, no. 3 (1980), pp Mosteller, F., Fifty Challenging Problems in Probability with Solutions, Reading, Mass: Addison-Wesley, O Connor, J.J. and Robertson, E.F., MacTutor History of Mathematics Archive [online], Available: URL 49.Namboodiri, K. and Suchindran, C., Life Table Techniques and Their Applications, Orlando: Academic Press, Patel, J.K. and Read, C.B., Handbook of the Normal Distribution, New York: Marcel Dekker, Peterson, I., The Jungles of Randomness: Mathematics and the Edge of Certainty, London: Penguin Books, Praetz, P.D., Australian share prices and the random walk hypothesis, Australian Journal of Statistics, v. 11, no.3 (1969), pp Råde, L. and Westergren, B., Beta β Mathematics Handbook, 2nd ed., Lund: Studentlitterature, Rényi, A., Probability Theory, Budapest: Akadémiai Kiadó, Révész, P., Random Walk in Random and Non-Random Environments, Singapore: World Scientific Press, Rosenthal, T.S., A First Look at Rigorous Probability Theory, Singapore: World Scientific Press. 57.Ross, S., A First Course in Probability, 5th ed., Upper Saddle River: Prentice Hall, Savage, R., Probability inequalities of the Tchebycheff type. Journal of Research of the National Bureau of Standards B. Mathematics and Mathematical Physics, vol. 65B, no.3, July September (1961), pp Sevastanyov, B., Christyakov, V., and Zubkov, A., Problems in the Theory of Probability, Moscow: Mir, Shiryaev, A.N., Probability, 2nd ed., New York: Springer, Shiryayev, A.N. (ed.) Selected Works of A.N. Kolmogorov, Vol. II: Probability Theory and Mathematical Statistics, Dordrecht: Kluwer Academic Publishers, Spitzer, F., Principles of Random Walk, 2nd ed., New York: Springer, 1976.

4 178 Bibliography 63.Stewart, J., Calculus, 4th ed. Pacific Grove: Brooks/Cole, Stoyanov, J., Counterexamples in Probability, 2nd ed. New York: John Wiley and Sons, Stoyanov, J., Mirazchiiski, I., Ignatov, Z. and Tanushev, M., Exercise Manual in Probability Theory, Dordrecht: Kluwer, Stuart, A. and Ord, K., Kendall s Advanced Theory of Statistics, 6th ed. Vol. 1, London: Edward Arnold, The Tattersall s Times, Issue 303, 26 September Tuckwell, H.C., Elementary Applications of Probability Theory, London: Chapman and Hall, Tversky, A. and Kahneman, D., Evidential impact of base rates. In Judgement Under Uncertainty: Heuristics and Biases. eds. D. Kahneman et al. Cambridge: Cambridge University Press, 1982, pp Uspensky, J.V., Introduction to Mathematical Probability, New York: McGraw- Hill, Whittaker, E.T. and Watson, G.N., A Course in Modern Analysis, 4th ed. Cambridge: Cambridge University Press, Wimmer, G. W. and Altman, G., Thesaurus of Univariate Discrete Probability Distributions, Essen: STAMM, 1999.

5 Index σ-algebra, 4 acceptable quality level, 33, 115 acceptance sampling, 114 Adams, W., 53 Altman, G., 26 AQL, 115 associative laws, 4 ballot theorem, 62 Bayes theorem, 11, 84, 85 Beckman, J., 96 Bennett, D., 11 Bharucha-Reid, A., 142 birthdays, 17, 93, 94 Box, G., 128 Breiman, L., 158 Buffon s needle, 45, 140 Butzer, P., 112 central limit theorem, 53, 55 characteristic function, 165 characteristic function, 26, 39, 52, 54, 153, 154 Chatfield, C., 174 Chebyshev, P., 32 Christyakov, V., 16 Clark, R., 16 complement, 4 conditional probability, 11, 84 correlation, 26, 39 covariance, 26, 39 Cox, D., 59 De Morgan s laws, 4 demography, 96 distribution function, 37 distributions t, 43, 131 binomial, 27, 30, 50, 51, 106 Cauchy, 40, 44, 132 continuous, 37, 121 discrete, 25, 101 exponential, 45, 112 Gamma, 40 geometric, 27 hypergeometric, 27, 30, 109 log normal, 45, 138 Normal, 40, 42, 43, 53, 124, 129, 154 Pareto, 44, 135 Poisson, 27, 30, 32, 50, 51, 58, 107, 113, 166 skewed, 130 uniform, 30, 40, 43, 108, 128 distributive laws, 4 double sampling plans, 116 Durrett, R., 157 e,

6 180 Index empirical rule, 43, 130 Epstein, R., 22 error function, 42 event, 5 expected value, 26, 39 Feller, W., 32 Freund, J., 127 gambler s ruin, 63 gamma function, 41, 122 geometric probability, 140 Hald, A., 114 Halmos, P., 7 Hammersley, J., 109 Handscomb, D., 109 Harward, P., 111 Henze, N., 16 Heyde, C., 48, 141 Ignatov, Z., 10, 155 independent events, 5 indicator function, 6, 70, 72 inequality Bonferroni, 8 Boole, 8, 75 Chebyshev, 31, 44, 56, 111, 134 triangle, 9, 77, 79 Jacod, J., 134 Jones, B., 135, 141 Jongmans, F., 112 Kahaner, D., 139 Kahneman, D., 11 Keyfitz, N., 96 Kolmogorov, A., 74, 134 life table, 18 21, 95 limit theorems, 47, 143 limits of sets, 10, 80 Lukacs, E., 52 Maor, E., 149 median, 37 Miller, H., 59 Mills, T., 111 Mirazchiiski, I., 10, 155 Mitra, A., 33 Moler, C., 139 moment generating function, 26, 39 Monte Carlo, 30, 109, 111 Moran, P., 48, 54, 140 mortality rate, 96 Mosteller, F., 16 Muller, M., 128 Namboodiri, K., 95 Nash, S., 139 number theory, 90 operating characteristic, 33, 115 Pareto, V., 135 Patel, J., 42, 140 perception of risk, 85 Perles, B., 127 Poker, 22, 23, 96 portfolio analysis, 28, 102 probability density function (pdf), 38 probability function, 26 probability measure, 4 probability space, 5 Protter, P., 134 psychology, 85 quality control, 33, 50, 57, 114 Rényi, A., 5 random polynomials, 45, 141 random walk, 59, 167 Read, C., 42, 140 reflection principle, 61, 168 Riedwyl, H., 16 ring, 7, 73 Rosenthal, T., 134 Ross, S., 57

7 Index 181 Sambandham, M., 142 sample space, 5 sampling plan double, 34 single, 33, 114 Savage, R., 32 Seneta, E., 141 sequences, 5 Sevastanyov, B., 16 Shiryaev, A., 134, 156 Simpson s rule, 139 simulation, 138 Sloane, N., 67 standard deviation, 26 Stewart, J., 139 Stirling s formula, 47, 143 Stoyanov, J., 9, 10, 44, 155 strategic planning, 56 strikes, 35 Suchindran, C., 95 symbolic logic, 81 Tanushev, M., 10, 155 Tattslotto, 15, 57 taxis, 12 telephone numbers, 14, 88 Tuckwell, H., 33 Tversky, A., 11 Uspensky, J., 18 variance, 26, 39 Wallis formula, 49, 148 Watson, G.N., 126 weak convergence, 53 weak law of large numbers, 51, 152 Weldon, W., 35, 119 Whittaker, E., 126 Wimmer, G., 26 zeta function, 101 Zubkov, A., 16