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Random signals and Processes ref: F. G. Stremler, Introduction to Communication Systems 3/e

Random signals and Processes ref: F. G. Stremler, Introduction to Communication Systems 3/e. Probability All possible outcomes (A 1 to A N ) are included Joint probability Conditional probability. Examples. Bayes’ theorem

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Random signals and Processes ref: F. G. Stremler, Introduction to Communication Systems 3/e

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  1. Random signals and Processesref: F. G. Stremler, Introduction to Communication Systems 3/e • Probability • All possible outcomes (A1 to AN) are included • Joint probability • Conditional probability Ya Bao Fundamentals of Communications theory

  2. Examples • Bayes’ theorem • Random 2/52 playing cards. After looking at the first card, P(2nd is heart)=? if 1st is or isn’t heart • Probability of two mutually exclusive events P(A+B)=P(A)+P(B) • If the events are not mutually exclusive P(A+B)=P(A)+P(B)-P(AB) Ya Bao Fundamentals of Communications theory

  3. Random variables • A real valued random variable is a real-value function defined on the events of the probability system. • Cumulative distribution function (CDF) of x is • Properties of F(a) • Nondecreasing, • 0<=F(a)<=1, Ya Bao Fundamentals of Communications theory

  4. Probability density function (PDF) Properties of PDF Ya Bao Fundamentals of Communications theory

  5. Discrete and continuous distributions • Discrete: random variable has M discrete values CDF or F(a) was discontinuous as a increase Digital communications PDF CDF Ya Bao Fundamentals of Communications theory

  6. Continuous distributions: if a random variable is allowed to take on any value in some interval. • CDF and PDF would be continuous functions. • Analogue communications, noise. • Expected value of a discretely distributed random variable Normalized average power Ya Bao Fundamentals of Communications theory

  7. Important distributions • Binomial • Poisson • Uniform • Gaussian • Sinusoidal Ya Bao Fundamentals of Communications theory

  8. Ya Bao Fundamentals of Communications theory

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