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ch5_rv_handout

# ch5_rv_handout - EEN 404 Communication Systems Ch5...

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1 EEN 404 Communication Systems 1 Ch5 Probability and Random Variable Random Variables (r.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) 2 • 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? x 01 F X (x) p 1 • 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) • Define: for continuous r.v., pdf is given as 3 then the cdf is given as the area under the pdf from - to x • Properties:

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2 • Example (uniform random variable): If X is equally likely to lie anywhere in the interval [a,b] , we say X is uniformly distributed on [a,b] , writing for shorthand as X U[a,b] .
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ch5_rv_handout - EEN 404 Communication Systems Ch5...

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