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Probability distribution, discrete random variables

Probability distribution, discrete random variables -...

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1 Probability Distributions, Discrete Random Variables Objectives: (Chapter 5, DeCoursey) - To define a probability function, cumulative probability, probability distribution function and cumulative distribution functions. - To define expectation and variance of a random variable. - To determine probabilities by using Binomial Distribution. Probability Distributions, Discrete Random Variables Probability function: Consider a random discrete variable, X, which can only take on certain values within an can only take on certain values within an interval of interest, such as x 0 , x 1 , x 2 , …x k , The corresponding probabilities are p(x 0 ), p(x 1 ), p(x 2 ),… p(x k ). Then p(x i ) (i=0,1,…k) or Pr[X=x i ] is called a probability function. 0 ) ( i x p 1 ) ( 0 = = k i i x p Probability Distributions, Discrete Random Variables Probability Function: The graph or table listing the various values of p(x i ) is the probability distribution function for the variable x. (e.g. tossing 2 fair coins) X, no. of heads Probability, p(x) 0 1/4 1 2/4 2 1/4 Total 1 0 1 2 0.25 0.5
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