References & Further Reading

References

1. J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006

   Course textbook. Chapters 5–6 cover joint distributions, independence, and transformations.

2. D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability, Athena Scientific, 2nd ed., 2008

   Excellent intuitive treatment of conditional distributions and expectation.

3. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, 4th ed., 2002

   Classic reference with many worked examples on joint distributions.

4. H. A. David and H. N. Nagaraja, Order Statistics, Wiley, 3rd ed., 2003

   Definitive reference on order statistics, including joint distributions and applications.

5. D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005

   Wireless applications of order statistics (diversity combining) and conditional expectation.

6. S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice Hall, 1993

   MMSE estimation via conditional expectation.

7. S. M. Stigler, The History of Statistics: The Measurement of Uncertainty before 1900, Harvard University Press, 1986

   Historical development of correlation and regression.

8. A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, 1933

   The axiomatic foundations of probability, including the formal definition of independence.

9. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, 2nd ed., 1997

   FFT-based convolution computation.

10. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, 2nd ed., 1971

    Advanced treatment of joint distributions, characteristic functions, and limit theorems.

11. M. Koller, B. Fesl, and G. Caire, A Scalable Bayesian MIMO Channel Estimator, 2022

    CommIT group contribution applying Bayesian conditional distributions to channel estimation.

12. S. M. Ross, A First Course in Probability, Pearson, 10th ed., 2019

    Accessible introduction to joint distributions with many examples.

Further Reading

• Copulas and dependence modeling beyond correlation

  R. B. Nelsen, An Introduction to Copulas, Springer, 2006

  Copulas separate the marginal distributions from the dependence structure, providing a richer framework than correlation alone.

• Multivariate Gaussian and its conditional structure

  Chapter 8 of this book

  The bivariate and multivariate Gaussian are the most important joint distributions in engineering — Chapter 8 develops the full theory.

• Extreme value theory

  S. Coles, An Introduction to Statistical Modeling of Extreme Values, Springer, 2001

  Order statistics lead naturally to extreme value distributions (Gumbel, Frechet, Weibull), which model the tails of distributions and are used in reliability and outage analysis.