ch9 - Ch 9 Distributions alreadystudied, values...

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1 Ch Continuous Probability  Distributions • Unlike a  discrete random   variable   which we have  already studied, a  continuous random variable  is  one that can assume an  uncountable  number of  values.  We cannot list the possible values because there is an  infinite number of them.  Because there is an infinite number of values, the  probability of each individual value is virtually 0.
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2 Because there is an infinite number of values, the  probability of each individual value is virtually 0. Thus, we can determine the probability of a  range of  values  only. • E.g. with a  discrete  random variable like tossing a die,  it is  meaningful to talk about P(X=5), say. • In a  continuous  setting (e.g. with time as a random  variable), the probability the random variable of  interest, say task length, takes  exactly  5 minutes is  infinitesimally small, hence P(X=5) = 0. It is meaningful to talk about P(X ≤ 5).
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3 Probability Density Function (pdf) A function f(x) is called a  probability density function   (over the range  a ≤ x ≤ b  if it meets the following  requirements: f ( x) x b a ar ea=1 1) f(x) ≥ 0 for all  x  between  a  and  b , and 2) The total area under the curve between  a  and  b  is  1.0
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Uniform Distribution Consider the  uniform probability distribution   (sometimes called the  rectangular probability  distribution ). It is described by the function:
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ch9 - Ch 9 Distributions alreadystudied, values...

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