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Chapter 6 Continous Probability Distributions

# Chapter 6 Continous Probability Distributions - Chapter 6...

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Chapter 6 – Continuous Probability Distributions pp. 224-228 Uniform Probability Distribution - If the probability of an event in any one given interval is equal to the probability of the event in any other equal interval in a given larger interval, the random variable x is said to have a uniform probability distribution - The uniform probability density function is then: f(x) = {1/(b-a)} for a ≤ x ≤ b , 0 elsewhere (Equation 6.1 pp.225) - ex: if in an interval from120 to 140 minutes, the probability of an event in any one- minute interval is equal to the even occurring in any other one-minute interval, then f(x) = {1/20} for 120 ≤ x ≤ 140, and 0 for elsewhere. Area as a Measure of Probability - The area under the graph of f(x) in a uniform probability distribution is equal to the probability. Area is equal to the height f(x) (probability) times the width of the interval - The total area under the graph of f(x) in a uniform probability distribution is equal to 1 (this holds true for all continuous probability distributions and is the analog of the condition that the sum of the probabilities must equal 1 for a discrete probability function) - The expected value of a uniform continuous probability distribution is E(x) = (a + b) / 2 , and the variance is

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Chapter 6 Continous Probability Distributions - Chapter 6...

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