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Additional Reading Material #2 1. Discrete Random Variables Example-1 (a 1-D random variable and its distribution): Tossing three fair coins (meaning: P{H}=p, with p=1/2), and record the total number of “Heads”from each tossing in a variable X. Æ a random variable This random variable is then a binomial distributed, X~B(n,p) with n=3 and p=1/2. Its behavior is summarized, by a 1-D probability mass function (pmf) as follows: Example-2 ( 2-D random variables and distribution): Tossing two fair coins and record each coin’s readouts in variables X and Y Æ two random variables or a 2-D random vector , whose behavior is summarized, by a 2-D probability mass function (pmf) as follows: For each individual coin (when looking at each coin’s results), the individual marginal distribution simply follows a Bernoulli model, i.e., 1, 1/ 2 (with a head showing up) 1/ 2 (with a head showing up) , 1 1/ 2 (with a tail showing up) 1 1/ 2 (with a tail showing up) pp XY qp ==   −= = = 

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