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Probability distribution, continuous random variables

# Probability distribution, continuous random variables -...

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1 Probability Distributions, Continuous Variables Objectives: (Chapter 6, DeCoursey) - To establish the difference between probability distribution for discrete and continuous distribution for discrete and continuous variables. - To learn how to calculate the probability that a random variable, X, will fall between the limits of “a” and “b”. A continuous variable, X, can take on an infinite number of values over a particular interval [a, b]. Probability Distributions, Continuous Variables f(x) The probability that the variable X will lie between theses two endpoints is given by = b a dx x f b x a ) ( ] Pr[ ([a, b] is sub-interval.) a b f(x) 0, f(x) is called probability density function. Probability Distributions, Continuous Variables a b f(x) = b a dx x f b x a ) ( ] Pr[ ([a, b] is sub-interval.) b x a i i x p ) ( Compared with discrete variable: Cumulative Distribution: The probability that the continuous random variable is less than some upper value, call it x 1 , is given by = 1 ) ( ] Pr[ 1 x dx x f x X Probability Distributions, Continuous Variables

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Probability distribution, continuous random variables -...

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