Chapter Five

Chapter Five - Lecture Notes Chapter Five Continuous Random...

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Lecture Notes Chapter Five: Continuous Random Variables Randall Miller 1 | Page 1. Continuous Probability Distributions The graphical form of the probability distribution for a continuous random variable x is a smooth curve. This curve, a function of x , is denoted by the symbol ( ) fx and is variously called a probability distribution function , a frequency function , or a probability distribution. The areas under a probability distribution correspond to probabilities for x . Let A be the area beneath the curve between two points, say, a and b . This area is the probability that x assumes a value between a and b ( ) axb << . Because there is no area over a single point, say, x = a , it follows that the probability associated with a particular value of x is equal to 0; that is, ( ) 0 Px a = = , and hence ( ) ( ) Pa x b Pa x b << = ≤≤ . Therefore, it does not matter whether the endpoints are included, it will not affect the probability. It follows that the total area under the probability distribution assigned to the set of all values of x – should equal 1.
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Chapter Five - Lecture Notes Chapter Five Continuous Random...

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