Abstract
Until now, all experiments E have had discrete events {A n} as their outputs, as in rolls of a die. On the other hand, everyday experience tells us that continuously random events often occur, as in the waiting time t for a train, or the position x at which a photon strikes the image plane.
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References
E.L. O’Neill: Introduction to Statistical Optics (Addison-Wesley, Reading, MA 1963)
C. Dainty (ed.): Laser Speckle and Related Phenomena, 2nd ed., Topics in Applied Physics, Vol. 9 (Springer, Berlin, Heidelberg, New York 1982)
G.N. Plass et al.: Appl. Opt. 16, 643–653 (1977)
C. Cox, W. Munk: J. Opt. Soc. Am. 44, 838–850 (1954)
J.W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York 1968)
B.R. Frieden: J. Opt. Soc. Am. 57, 56 (1967)
S.Q. Duntley: J. Opt. Soc. Am. 53, 214–233 (1963)
D.M. Green, J.A. Swets: Signal Detection Theory and Psychophysics (Wiley, New York 1966)
J.A. Swets (ed.): Signal Detection and Recognition by Human Observers (Wiley, New York 1964)
C.H. Slump, H.A. Ferwerda: Optik 62, 98 (1982)
I.I. Hirschman: Am. J. Math. 79, 152 (1957)
W. Beckner: Ann. Math 102, 159 (1975)
S. Kullback: Information Theory and Statistics (Wiley, New York 1959)
A. Renyi: On Measures of Entropy and Information, Proc. of 4th Berkeley Symp. on Math., Stat, and Prob. Theory (Univ. of California Press, Berkeley 1961)
W.K. Wootters: Phys. Rev. D 23, 357 (1981)
C. Tsallis: J. Stat. Phys. 52, 479 (1988)
R.A. Fisher: Phil. Trans. R. Soc. Lond. 222, 309 (1922)
B.R. Frieden: J. Opt. Soc. Am. 73, 927–938 (1983)
D.G. Simpson, J. Amer. Stat. Assoc. 84, 107 (1989)
B.R. Frieden, Founds. of Phys. 29, 1521 (1999)
M.C. Alonso and M.A. Gil: in Advances in Intelligent Computing — IPMU’94, eds. B. Bouchon-Meunier et. al. (Springer-Verlag, Berlin 1994)
Additional Reading
Clarke, L. E.: Random Variables (Longman, New York 1975)
Feller, W.: An Introduction to Probability Theory and Its Applications, Vol.11 (Wiley, New York 1966)
Papoulis, A.: Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York 1965)
Pfeiffer, R. E.: Concepts of Probability Theory, 2nd rev. ed. (Dover, New York 1978)
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Frieden, B.R. (2001). Continuous Random Variables. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56699-8_3
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DOI: https://doi.org/10.1007/978-3-642-56699-8_3
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