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# ch5_rv - EEN 404 EEN 404 Communication Systems...

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Unformatted text preview: EEN 404 EEN 404 Communication Systems Communication Systems h5 Probability and Random h5 Probability and Random Ch5 Probability and Random Ch5 Probability and Random Variable Variable 1 Random Variables (r.v.) do V b es ( .v.) Types discrete r.v. , e.g., the result of tossing of a coin (head or tail) continuous r.v., e.g., the direction of spinning of a pointer (0 – 2 ) Cumulative distributed function (cdf) • Define: cdf F X (x) = probability (X ≤ x) := P(X ≤ x) • Property: 0 ≤ F X (x) ≤ 1 , with F X (- ∞ )=0, F X ( ∞ )=1 • Example: Binary r.v. X taking on values {0,1} with probability p and 1-p , respectively, where 0 ≤ p ≤ 1. What is the cdf of X? ) F X (x) p 1 2 x 1 iscrete r v X taking on values {x with probability { respectively • Discrete r.v. X taking on values {x i } with probability { p i } , respectively, then the cdf of X is given as Probability density function (pdf) efine: for continuous r v pdf is given as • Define: for continuous r.v., pdf is given as then the cdf is given as the area under the pdf from - ∞ to x • Properties: 3 • Example (uniform random variable): If...
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ch5_rv - EEN 404 EEN 404 Communication Systems...

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